Trend Correlation Oscillator [SS]Hello,
Publishing this simple indicator.
What is it?
The Trend Correlation Oscillator takes the concept of my autocorrelation oscillator but applies it simply to time instead of autocorrelation.
It performs a correlation assessment to time. The theory behind it is the stronger the correlation, the more "exhausted" the trend and the more likely the trend will reverse. It is kind of building off of random walk theory in which the market should be random and efficient.
Does it work?
If you follow me on my indicator side, you will know that my indicators are all based on my own research and findings and stuff that I personally find that works. All of this comes from years of losing money trying to use conventional systems and finally developing my own stuff that I find works well. This is such an invention. It does work extremely well but its best applied for day traders. If you want to use this as a swing trader, play around with the lookback length. I don't have general recommendations to swing traders wanting to use this because this isn't an indicator I personally would use for swing trading (I would use the autocorrelation oscillator for that).
How to use it:
The default setting is to a 14 candle lookback. This works the best. It also should really be used on the 5 minute chart and not the 1 minute chart, as from my experience this works much better.
When a trend is approaching "exhaustion" to the upside, the indicator will turn red to let you know we are approaching a trend exhaustion. Once the exhaustion is at its peak and beginning to reverse, the indicator will place a cross symbol on where your entry should be. See the image below for an example:
It also works well if you combine it with my PTCR Correlation Indicator:
Closing thoughts
That is basically the indicator. Its one of my more simple ones, but many times simple is better and most effective!
Hopefully you find it helpful.
As always let me know your questions, comments and feedback/recommendations for improvements below.
Please know I do read and make note of all recommendations for indicators and improvements, however as it is just me managing them, it takes time for implementation and review :-).
Safe trades!
Tìm kiếm tập lệnh với "TAKE"
Liquidity Voids (FVG) [LuxAlgo]The Liquidity Voids (FVG) indicator is designed to detect liquidity voids/imbalances derived from the fair value gaps and highlight the distribution of the liquidity voids at specific price levels.
Fair value gaps and liquidity voids are both indicators of sell-side and buy-side imbalance in trading. The only difference is how they are represented in the trading chart. Liquidity voids occur when the price moves sharply in one direction forming long-range candles that have little trading activity, whilst a fair value is a gap in price.
🔶 USAGE
Liquidity can help you to determine where the price is likely to head next. In conjunction with higher timeframe market structure, and supply and demand, liquidity can give you insights into potential price movement. It's essential to practice using liquidity alongside trend analysis and supply and demand to read market conditions effectively.
The peculiar thing about liquidity voids is that they almost always fill up. And by “filling”, we mean the price returns to the origin of the gap. The reason for this is that during the gap, an imbalance is created in the asset that has to be made up for. The erasure of this gap is what we call the filling of the void. And while some voids waste no time in filling, some others take multiple periods before they get filled.
🔶 SETTINGS
The script takes into account user-defined parameters and detects the liquidity voids based on them, where detailed usage for each user-defined input parameter in indicator settings is provided with the related input's tooltip.
🔹 Liquidity Detection
Liquidity Voids Threshold: Act as a filter while detecting the Liquidity Voids. When set to 0 basically means no filtering is applied, increasing the value causes the script to check the width of the void compared to a fixed-length ATR value
Bullish: Color customization option for Bullish Liquidity Voids
Bearish: Color customization option for Bearish Liquidity Voids
Labels: Toggles the visibility of the Liquidity Void label
Filled Liquidity Voids: Toggles the visibility of the Filled Liquidity Voids
🔹 Display Options
Mode: Controls the lookback length of detection and visualization
# Bars: Lookback length customization, in case Mode is set to Present
🔶 RELATED SCRIPTS
Buyside-Sellside-Liquidity
Fair-Value-Gaps
Bar Dependent Moving AverageImagine using an exercising strategy from a gym coach who retired 10 years ago as there dozens of other trainers who constantly try to adapt and find a better approach. You would be missing out.
It's the same with using fixed periods, you just look back.
How about an exercising strategy from a gym coach who is simultaneously trying to adapt himself?
How could you figure out a strategy that adapts with the market as the market is indirectly finding a better approach to take you out?
Relative Moving Averages simply speaking count the total amount of bars and divide it by the period for which you want to use the moving average. Instead of looking at the last X bars, it divides the total amount of bars / X as the moving average period.
It takes all bars into account, the entire chart history essentially turning it into an adaptive moving average, in the example mentioned above into an adaptive exercising strategy.
The Bar Dependent Moving Average Periods are 2,3,5,8 etc., i.e. the entire fibonacci sequence up to 4181.
The white line is the relative fibonacci moving average, which is calculated by adding all Fibonacci Bar Dependent Moving Averages with one another / by the total amount of fibonacci numbers used i.e. 18.
The bar-dependent fibonacci moving average is upon further investigation (on shorter timeframes <30m) a useful support/resistance indicator since the price tends to wick/consolidate or fully break through the fibonoacci bar dependent moving average.
If there are more than 5000 bars of Candlestick data enable the lock in the settings menu to limit the maximum last X bars back to 5000 to make it possible for Tradingview to run the script since Tradingview does not allow it to look more than 5000 bars back.
Custom Fib by Dr. MauryaThis indicator is based on purely Fibonacci levels.
How it works:
Let's first understand the Fibonacci levels.
The main Fibonacci numbers are 0, 0.236, 0.392, 0.5, 0.618, 0.764, 1 whereas 0 equal to low and 1 equal to high.
As the market is moving in any direction, new lows or new highs are developing and hence Fibonacci levels are also changing throughout the time.
Sometime market retraces from various levels like 0.5, 0.618/0.382(mirror value), 0.762/0.236 (mirror value).
Retracement : The three mid-level 0.382, 0.5 and 0.618 are act as a retracement or like pivot levels for market. These levels are filled with green and red colors to attention the buyers and sellers to take a trade either side if any candlestick pattern are observed at these levels.
one direction trend takes support of 0.236/0.786(mirror value) (blue line in chart)
Sometime buy/sell on dip levels are happen at 0.762/0.392 (mirror value).
Targets: Target could be Fibonacci extension level lowest targets (1, 1.18, 1.23,), medium targets (1.39, 1.5, 1.61) and large target (2.0, 2.5.2.61, 3.0) as depended on your study volume levels and trend strength.
Stoploss: You can choose any preceding lines for stoploss: e.g. if you enter long on 0.618 or 0.5 levels you can set SL on 0.762
Previous day three mid-point 0.382, 0.5, 0.618 (filled with red and green color) as well as high and low could also act as resistance or support levels for current day market.
Lets understand the Input section of indicator
The first input section allowed to choose where you want to start developing Fibonacci : select session for intraday then weekly, monthly and yearly options are available.
Now you can set any Fibonacci levels (as you wish) you can set upto 20 levels.
By default, total 7 Fibonacci levels are plotted (0, 0.236, 0.392, 0.618, 0.762 and 1.
Further you can set Fibonacci extension level for long side (1.18, 1.23, 1.39, 1.5, 1.61, 2 etc).
You must be careful when you enter Fibonacci extension level lower side (short side). You need to enter value -0.5 (equal to 1.5 for long). -0.618 (equal to 1.618 for long), -1(equal to 2.0 for long).
You can fill color between any two adjacent lines from style sections.
You can also select labels from input tab if you want to see Fibonacci numbers on chart as labels.
You can also shift the labels from current bar to desired offset bar by changing the value in input section.
Conclusion
This indicator is highly customisable developing Fibonacci levels because everyone and different scripts works on different fib levels.
This indicator keeps the Fibonacci levels at a particular time and it plots only new lines when new low or high established without affecting the previous Fibonacci levels. Overall, as the market moves, you will find the trending plot goes which side.
Selective Moving Average: DemoThis indicator produces a conditional moving average based off of your chosen inputs. For example, you can create an EMA that only takes into account closing prices when the 14 period RSI is greater than 50, or a VWMA that tracks hl2 values when the hl2 value is within one standard deviation from the mean. The possibilities are highly configurable to your liking. Please comment below additional conditions you might like me to add to the moving average and I will try my best to get to your feedback.
The following parameters are configurable:
--> Source: This is the source of the moving average that you want to create. You can use external sources if you have another indicator on your chart.
--> Condition: This is the condition that you want to take into account when the moving average is calculating itself. For instance, I have the following conditions pre-built (more to come): Source within 1 standard deviation of the mean (of the source), Source within 2 standard deviations of the mean (of the source), Positive volume, Negative volume, RSI greater than 50, RSI less than 50, Candlestick length greater than body.
--> Length: The length of the selective moving average. For conditions that occur infrequently, a larger length may be necessary to improve accuracy.
--> Average type: The type of moving average (SMA, EMA, RMA, etc.) that you wish to create
--> Condition length: An optional parameter if you are using a condition that depends on a length itself, i.e. the RSI - here you can change the RSI length. The RSI source will be the moving average source, but future updates may separate the two.
Weekly Range Support & Resistance Levels [QuantVue]Weekly Range Support & Resistance Levels
Description:
The Weekly Range Support & Resistance Levels analyzes weekly ranges and takes the average range of the last 30 weeks (default setting).
It also takes the average +/- a standard deviation, and creates support & resistance levels/zones based on the weekly opening price.
The levels will update each week, and previous weekly levels can be toggled on or off.
Settings:
🔹Averaging Period
🔹Standard Deviation Multiplier
🔹Toggle Support & Resistance Prices
🔹Show Weekly Open Line
🔹Show Previous Levels
Don't hesitate to reach out with any questions or concerns. We hope you enjoy!
Cheers.
Script TimerWanna know how long your script takes to execute.
Just put this function at the end of your code and it will tell you how much time it takes to run your algo from start to end.
Data will show in the data window panel measured in seconds
Machine Learning : Cosine Similarity & Euclidean DistanceIntroduction:
This script implements a comprehensive trading strategy that adheres to the established rules and guidelines of housing trading. It leverages advanced machine learning techniques and incorporates customised moving averages, including the Conceptive Price Moving Average (CPMA), to provide accurate signals for informed trading decisions in the housing market. Additionally, signal processing techniques such as Lorentzian, Euclidean distance, Cosine similarity, Know sure thing, Rational Quadratic, and sigmoid transformation are utilised to enhance the signal quality and improve trading accuracy.
Features:
Market Analysis: The script utilizes advanced machine learning methods such as Lorentzian, Euclidean distance, and Cosine similarity to analyse market conditions. These techniques measure the similarity and distance between data points, enabling more precise signal identification and enhancing trading decisions.
Cosine similarity:
Cosine similarity is a measure used to determine the similarity between two vectors, typically in a high-dimensional space. It calculates the cosine of the angle between the vectors, indicating the degree of similarity or dissimilarity.
In the context of trading or signal processing, cosine similarity can be employed to compare the similarity between different data points or signals. The vectors in this case represent the numerical representations of the data points or signals.
Cosine similarity ranges from -1 to 1, with 1 indicating perfect similarity, 0 indicating no similarity, and -1 indicating perfect dissimilarity. A higher cosine similarity value suggests a closer match between the vectors, implying that the signals or data points share similar characteristics.
Lorentzian Classification:
Lorentzian classification is a machine learning algorithm used for classification tasks. It is based on the Lorentzian distance metric, which measures the similarity or dissimilarity between two data points. The Lorentzian distance takes into account the shape of the data distribution and can handle outliers better than other distance metrics.
Euclidean Distance:
Euclidean distance is a distance metric widely used in mathematics and machine learning. It calculates the straight-line distance between two points in Euclidean space. In two-dimensional space, the Euclidean distance between two points (x1, y1) and (x2, y2) is calculated using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).
Dynamic Time Windows: The script incorporates a dynamic time window function that allows users to define specific time ranges for trading. It checks if the current time falls within the specified window to execute the relevant trading signals.
Custom Moving Averages: The script includes the CPMA, a powerful moving average calculation. Unlike traditional moving averages, the CPMA provides improved support and resistance levels by considering multiple price types and employing a combination of Exponential Moving Averages (EMAs) and Simple Moving Averages (SMAs). Its adaptive nature ensures responsiveness to changes in price trends.
Signal Processing Techniques: The script applies signal processing techniques such as Know sure thing, Rational Quadratic, and sigmoid transformation to enhance the quality of the generated signals. These techniques improve the accuracy and reliability of the trading signals, aiding in making well-informed trading decisions.
Trade Statistics and Metrics: The script provides comprehensive trade statistics and metrics, including total wins, losses, win rate, win-loss ratio, and early signal flips. These metrics offer valuable insights into the performance and effectiveness of the trading strategy.
Usage:
Configuring Time Windows: Users can customize the time windows by specifying the start and finish time ranges according to their trading preferences and local market conditions.
Signal Interpretation: The script generates long and short signals based on the analysis, custom moving averages, and signal processing techniques. Users should pay attention to these signals and take appropriate action, such as entering or exiting trades, depending on their trading strategies.
Trade Statistics: The script continuously tracks and updates trade statistics, providing users with a clear overview of their trading performance. These statistics help users assess the effectiveness of the strategy and make informed decisions.
Conclusion:
With its adherence to housing trading rules, advanced machine learning methods, customized moving averages like the CPMA, and signal processing techniques such as Lorentzian, Euclidean distance, Cosine similarity, Know sure thing, Rational Quadratic, and sigmoid transformation, this script offers users a powerful tool for housing market analysis and trading. By leveraging the provided signals, time windows, and trade statistics, users can enhance their trading strategies and improve their overall trading performance.
Disclaimer:
Please note that while this script incorporates established tradingview housing rules, advanced machine learning techniques, customized moving averages, and signal processing techniques, it should be used for informational purposes only. Users are advised to conduct their own analysis and exercise caution when making trading decisions. The script's performance may vary based on market conditions, user settings, and the accuracy of the machine learning methods and signal processing techniques. The trading platform and developers are not responsible for any financial losses incurred while using this script.
By publishing this script on the platform, traders can benefit from its professional presentation, clear instructions, and the utilisation of advanced machine learning techniques, customised moving averages, and signal processing techniques for enhanced trading signals and accuracy.
I extend my gratitude to TradingView, LUX ALGO, and JDEHORTY for their invaluable contributions to the trading community. Their innovative scripts, meticulous coding patterns, and insightful ideas have profoundly enriched traders' strategies, including my own.
VWAP Open Session Anchored by HampehThe VWAP Open Session Anchored indicator differs from traditional VWAP indicators by automatically anchoring the Volume Weighted Average Price calculation to three market session starts Morning, Evening, and Night. Each session represents a distinct time period within the trading day, offering traders and investors a more comprehensive view of the volume-weighted average price within specific sessions.
What Is the Volume-Weighted Average Price (VWAP)?
The volume-weighted average price (VWAP) is a technical analysis indicator used on intraday charts that resets at the start of every new trading session.
VWAP is important because it provides traders with pricing insight into both the trend and value of a security.
KEY TAKEAWAYS
1. The volume-weighted average price (VWAP) is a single line on intraday charts.
2. It looks similar to a moving average line but smoother.
3. VWAP represents a view of price action throughout a single day's trading session.
4. Retail and professional traders may use the VWAP to help them determine intraday price trends.
5. VWAP typically is most useful to short-term traders.
VWAP is calculated by totaling the dollars traded for every transaction (price multiplied by the volume) and then dividing by the total shares traded.
VWAP = Cumulative Typical Price x Volume/Cumulative Volume
Where Typical Price = High price + Low price + Closing Price/3
Cumulative = total since the trading session opened.
How Is VWAP Used?
VWAP is used in different ways by traders. Traders may use VWAP as a trend confirmation tool and build trading rules around it. For instance, they may consider stocks with prices below VWAP as undervalued and those with prices above it, as overvalued. If prices below VWAP move above it, traders may go long on the stock. If prices above VWAP move below it, they may sell their positions or initiate short positions.
Institutional buyers including mutual funds use VWAP to help move into or out of stocks with as small of a market impact as possible. Therefore, when they can, institutions will try to buy below the VWAP or sell above it. This way their actions push the price back toward the average, instead of away from it.
Source: www.investopedia.com
Nonlinear Regression, Zero-lag Moving Average [Loxx]Nonlinear Regression and Zero-lag Moving Average
Technical indicators are widely used in financial markets to analyze price data and make informed trading decisions. This indicator presents an implementation of two popular indicators: Nonlinear Regression and Zero-lag Moving Average (ZLMA). Let's explore the functioning of these indicators and discuss their significance in technical analysis.
Nonlinear Regression
The Nonlinear Regression indicator aims to fit a nonlinear curve to a given set of data points. It calculates the best-fit curve by minimizing the sum of squared errors between the actual data points and the predicted values on the curve. The curve is determined by solving a system of equations derived from the data points.
We define a function "nonLinearRegression" that takes two parameters: "src" (the input data series) and "per" (the period over which the regression is calculated). It calculates the coefficients of the nonlinear curve using the least squares method and returns the predicted value for the current period. The nonlinear regression curve provides insights into the overall trend and potential reversals in the price data.
Zero-lag Moving Average (ZLMA)
Moving averages are widely used to smoothen price data and identify trend directions. However, traditional moving averages introduce a lag due to the inclusion of past data. The Zero-lag Moving Average (ZLMA) overcomes this lag by dynamically adjusting the weights of past values, resulting in a more responsive moving average.
We create a function named "zlma" that calculates the ZLMA. It takes two parameters: "src" (the input data series) and "per" (the period over which the ZLMA is calculated). The ZLMA is computed by first calculating a weighted moving average (LWMA) using a linearly decreasing weight scheme. The LWMA is then used to calculate the ZLMA by applying the same weight scheme again. The ZLMA provides a smoother representation of the price data while reducing lag.
Combining Nonlinear Regression and ZLMA
The ZLMA is applied to the input data series using the function "zlma(src, zlmaper)". The ZLMA values are then passed as input to the "nonLinearRegression" function, along with the specified period for nonlinear regression. The output of the nonlinear regression is stored in the variable "out".
To enhance the visual representation of the indicator, colors are assigned based on the relationship between the nonlinear regression value and a signal value (sig) calculated from the previous period's nonlinear regression value. If the current "out" value is greater than the previous "sig" value, the color is set to green; otherwise, it is set to red.
The indicator also includes optional features such as coloring the bars based on the indicator's values and displaying signals for potential long and short positions. The signals are generated based on the crossover and crossunder of the "out" and "sig" values.
Wrapping Up
This indicator combines two important concepts: Nonlinear Regression and Zero-lag Moving Average indicators, which are valuable tools for technical analysis in financial markets. These indicators help traders identify trends, potential reversals, and generate trading signals. By combining the nonlinear regression curve with the zero-lag moving average, this indicator provides a comprehensive view of the price dynamics. Traders can customize the indicator's settings and use it in conjunction with other analysis techniques to make well-informed trading decisions.
Purple CloudThe above lines calculate several intermediate values used in the indicator's calculations. Here's a breakdown of each variable:
a1: Represents a modified Exponential Moving Average (EMA) of the high price series, subtracted by a Simple Moving Average (SMA) of the low price series.
a2: Takes the square root of the lowest value between the highest close price over the last 200 bars and the current close price, multiplied by a1.
b1: Represents a modified EMA of the low price series, subtracted by an SMA of the high price series.
b2: Takes the square root of the highest value between the lowest close price over the last 200 bars and the current close price, multiplied by b1.
c1: Represents the square root of a2 multiplied by b2.
These lines create multiple plots using the plot function. Each plot represents a displaced version of c1 by a certain multiple of the Average True Range (ATR) multiplied by a constant factor (0.1, 0.2, 0.3, etc.). The transparency (transp) is set to 100 for all plots.
Pattern Forecast (Expo)█ Overview
The Pattern Forecast indicator is a technical analysis tool that scans historical price data to identify common chart patterns and then analyzes the price movements that followed these patterns. It takes this information and projects it into the future to provide traders with potential price actions that may occur if the same pattern is identified in real-time market data. This projection helps traders to understand the possible outcomes based on the previous occurrences of the pattern, thereby offering a clearer perspective of the market scenario. By analyzing the historical data and understanding the subsequent price movements following the appearance of a specific pattern, the indicator can provide valuable insights into potential future market behavior.
█ Calculations
The indicator works by scanning historical price data for various candlestick patterns. It includes all in-built TradingView patterns, credit to TradingView that has coded them.
Essentially, the indicator takes the historical price moves that followed the pattern to forecast what might happen next.
█ Example
In this example, the algorithm is set to search for the Inverted Hammer Bullish candlestick pattern. If the pattern is found, the historical outcome is then projected into the future. This helps traders to understand how the past pattern evolved over time.
█ How to use
Providing traders with a comprehensive understanding of historical patterns and their implications for future price action allows them to assess the likelihood of specific market scenarios objectively. For example, suppose the pattern forecast indicator suggests that a particular pattern is likely to lead to a bullish move in the market. A trader might consider going long if the same pattern is identified in the real-time market. Similarly, a trader might consider shorting the asset if the indicator suggests a bearish move is likely, if the same pattern is identified in the real-time market.
█ Settings
Pattern
Select the pattern that the indicator should scan for. All inbuilt TradingView patterns can be selected.
Forecast Candles
Number of candles to project into the future.
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Disclaimer
The information contained in my Scripts/Indicators/Ideas/Algos/Systems does not constitute financial advice or a solicitation to buy or sell any securities of any type. I will not accept liability for any loss or damage, including without limitation any loss of profit, which may arise directly or indirectly from the use of or reliance on such information.
All investments involve risk, and the past performance of a security, industry, sector, market, financial product, trading strategy, backtest, or individual's trading does not guarantee future results or returns. Investors are fully responsible for any investment decisions they make. Such decisions should be based solely on an evaluation of their financial circumstances, investment objectives, risk tolerance, and liquidity needs.
My Scripts/Indicators/Ideas/Algos/Systems are only for educational purposes!
Chandelier Exit ZLSMA StrategyIntroducing a Powerful Trading Indicator: Chandelier Exit with ZLSMA
If you're a trader, you know the importance of having the right tools and indicators to make informed decisions. That's why we're excited to introduce a powerful new trading indicator that combines the Chandelier Exit and ZLSMA: two widely-used and effective indicators for technical analysis.
The Chandelier Exit (CE) is a popular trailing stop-loss indicator developed by Chuck LeBeau. It's designed to follow the price trend of a security and provide an exit signal when the price crosses below the CE line. The CE line is based on the Average True Range (ATR), which is a measure of volatility. This means that the CE line adjusts to the volatility of the security, making it a reliable indicator for trailing stop-losses.
The ZLEMA (Zero Lag Exponential Moving Average) is a type of exponential moving average that's designed to reduce lag and improve signal accuracy. The ZLSMA takes into account not only the current price but also past prices, using a weighted formula to calculate the moving average. This makes it a smoother indicator than traditional moving averages, and less prone to giving false signals.
When combined, the CE and ZLSMA create a powerful indicator that can help traders identify trend changes and make more informed trading decisions. The CE provides the trailing stop-loss signal, while the ZLSMA provides a smoother trend line to help identify potential entry and exit points.
In our indicator, the CE and ZLSMA are plotted together on the chart, making it easy to see both the trailing stop-loss and the trend line at the same time. The CE line is displayed as a dotted line, while the ZLSMA line is displayed as a solid line.
Using this indicator, traders can set their stop-loss levels based on the CE line, while also using the ZLSMA line to identify potential entry and exit points. The combination of these two indicators can help traders reduce their risk and improve their trading performance.
In conclusion, the Chandelier Exit with ZLSMA is a powerful trading indicator that combines two effective technical analysis tools. By using this indicator, traders can identify trend changes, set stop-loss levels, and make more informed trading decisions. Try it out for yourself and see how it can improve your trading performance.
Warning: The results in the backtest are from a repainting strategy. Don't take them seriously. You need to do a dry live test in order to test it for its useability.
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Here is a description of each input field in the provided source code:
length: An integer input used as the period for the ATR (Average True Range) calculation. Default value is 1.
mult: A float input used as a multiplier for the ATR value. Default value is 2.
showLabels: A boolean input that determines whether to display buy/sell labels on the chart. Default value is false.
isSignalLabelEnabled: A boolean input that determines whether to display signal labels on the chart. Default value is true.
useClose: A boolean input that determines whether to use the close price for extrema calculations. Default value is true.
zcolorchange: A boolean input that determines whether to enable rising/decreasing highlighting for the ZLSMA (Zero-Lag Exponential Moving Average) line. Default value is false.
zlsmaLength: An integer input used as the length for the ZLSMA calculation. Default value is 50.
offset: An integer input used as an offset for the ZLSMA calculation. Default value is 0.
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Ty for checking this out and good luck on your trading journey! Likes and comments are appreciated. 👍
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Credits to:
▪ @everget – Chandelier Exit (CE)
▪ @netweaver2022 – ZLSMA
MVRV Z ScoreIndicator Overview
MVRV Z-Score is a bitcoin chart that uses blockchain analysis to identify periods where Bitcoin is extremely over or undervalued relative to its 'fair value'.
It uses three metrics:
1. Market Value: The current price of Bitcoin multiplied by the number of coins in circulation. This is like market cap in traditional markets i.e. share price multiplied by number of shares.
2. Realised Value: Rather than taking the current price of Bitcoin, Realised Value takes the price of each Bitcoin when it was last moved i.e. the last time it was sent from one wallet to another wallet. It then adds up all those individual prices and takes an average of them. It then multiplies that average price by the total number of coins in circulation.
In doing so, it strips out the short term market sentiment that we have within the Market Value metric. It can therefore be seen as a more 'true' long term measure of Bitcoin value which Market Value moves above and below depending on the market sentiment at the time.
3. Z-score (Orange): A standard deviation test that pulls out the extremes in the data between market value and realised value.
How It Can Be Used
The MVRV Z-score has historically been very effective in identifying periods where market value is moving unusually high above realised value. These periods are highlighted by the z-score (red line) entering the pink box and indicates the top of market cycles. It has been able to pick the market high of each cycle to within two weeks.
It also shows when market value is far below realised value, highlighted by z-score entering the green box. Buying Bitcoin during these periods has historically produced outsized returns.
(Bar colors shows when market is trending down or a top - strong red or trending up and bottom - strong green. Added allerts for values)
Bitcoin Price Prediction Using This Tool
MVRV Z-Score bitcoin chart is useful for predicting Bitcoin price at the extremes of market conditions. It is able to forecast where Bitcoin price may need to pull back when MVRV Z-score enters the upper red band, and also when CRYPTOCAP:BTC price may rally after spending time in the lower green band.
Historically it has picked major Bitcoin price highs to within 2 weeks.
Created By
@aweandwonder who has unfortunately since deleted the original article and his online profile.
He built on the initial work to create MVRV by Murad Mahmudov and David Puell
Boxes_PlotIn the world of data visualization, heatmaps are an invaluable tool for understanding complex datasets. They use color gradients to represent the values of individual data points, allowing users to quickly identify patterns, trends, and outliers in their data. In this post, we will delve into the history of heatmaps, and then discuss how its implemented.
The "Boxes_Plot" library is a powerful and versatile tool for visualizing multiple indicators on a trading chart using colored boxes, commonly known as heatmaps. These heatmaps provide a user-friendly and efficient method for analyzing the performance and trends of various indicators simultaneously. The library can be customized to display multiple charts, adjust the number of rows, and set the appropriate offset for proper spacing. This allows traders to gain insights into the market and make informed decisions.
Heatmaps with cells are interesting and useful for several reasons. Firstly, they allow for the visualization of large datasets in a compact and organized manner. This is especially beneficial when working with multiple indicators, as it enables traders to easily compare and contrast their performance. Secondly, heatmaps provide a clear and intuitive representation of the data, making it easier for traders to identify trends and patterns. Finally, heatmaps offer a visually appealing way to present complex information, which can help to engage and maintain the interest of traders.
History of Heatmaps
The concept of heatmaps can be traced back to the 19th century when French cartographer and sociologist Charles Joseph Minard used color gradients to visualize statistical data. He is well-known for his 1869 map, which depicted Napoleon's disastrous Russian campaign of 1812 using a color gradient to represent the dwindling size of Napoleon's army.
In the 20th century, heatmaps gained popularity in the fields of biology and genetics, where they were used to visualize gene expression data. In the early 2000s, heatmaps found their way into the world of finance, where they are now used to display stock market data, such as price, volume, and performance.
The boxes_plot function in the library expects a normalized value from 0 to 100 as input. Normalizing the data ensures that all values are on a consistent scale, making it easier to compare different indicators. The function also allows for easy customization, enabling users to adjust the number of rows displayed, the size of the boxes, and the offset for proper spacing.
One of the key features of the library is its ability to automatically scale the chart to the screen. This ensures that the heatmap remains clear and visible, regardless of the size or resolution of the user's monitor. This functionality is essential for traders who may be using various devices and screen sizes, as it enables them to easily access and interpret the heatmap without needing to make manual adjustments.
In order to create a heatmap using the boxes_plot function, users need to supply several parameters:
1. Source: An array of floating-point values representing the indicator values to display.
2. Name: An array of strings representing the names of the indicators.
3. Boxes_per_row: The number of boxes to display per row.
4. Offset (optional): An integer to offset the boxes horizontally (default: 0).
5. Scale (optional): A floating-point value to scale the size of the boxes (default: 1).
The library also includes a gradient function (grad) that is used to generate the colors for the heatmap. This function is responsible for determining the appropriate color based on the value of the indicator, with higher values typically represented by warmer colors such as red and lower values by cooler colors such as blue.
Implementing Heatmaps as a Pine Script Library
In this section, we'll explore how to create a Pine Script library that can be used to generate heatmaps for various indicators on the TradingView platform. The library utilizes colored boxes to represent the values of multiple indicators, making it simple to visualize complex data.
We'll now go over the key components of the code:
grad(src) function: This function takes an integer input 'src' and returns a color based on a predefined color gradient. The gradient ranges from dark blue (#1500FF) for low values to dark red (#FF0000) for high values.
boxes_plot() function: This is the main function of the library, and it takes the following parameters:
source: an array of floating-point values representing the indicator values to display
name: an array of strings representing the names of the indicators
boxes_per_row: the number of boxes to display per row
offset (optional): an integer to offset the boxes horizontally (default: 0)
scale (optional): a floating-point value to scale the size of the boxes (default: 1)
The function first calculates the screen size and unit size based on the visible chart area. Then, it creates an array of box objects representing each data point. Each box is assigned a color based on the value of the data point using the grad() function. The boxes are then plotted on the chart using the box.new() function.
Example Usage:
In the example provided in the source code, we use the Relative Strength Index (RSI) and the Stochastic Oscillator as the input data for the heatmap. We create two arrays, 'data_1' containing the RSI and Stochastic Oscillator values, and 'data_names_1' containing the names of the indicators. We then call the 'boxes_plot()' function with these arrays, specifying the desired number of boxes per row, offset, and scale.
Conclusion
Heatmaps are a versatile and powerful data visualization tool with a rich history, spanning multiple fields of study. By implementing a heatmap library in Pine Script, we can enhance the capabilities of the TradingView platform, making it easier for users to visualize and understand complex financial data. The provided library can be easily customized and extended to suit various use cases and can be a valuable addition to any trader's toolbox.
Library "Boxes_Plot"
boxes_plot(source, name, boxes_per_row, offset, scale)
Parameters:
source (float ) : - an array of floating-point values representing the indicator values to display
name (string ) : - an array of strings representing the names of the indicators
boxes_per_row (int) : - the number of boxes to display per row
offset (int) : - an optional integer to offset the boxes horizontally (default: 0)
scale (float) : - an optional floating-point value to scale the size of the boxes (default: 1)
Price Extrapolator with Std DeviationPrice Extrapolator with Deviation Cones - A Powerful Tool for Predicting Future Prices
Subtitle: Discover how this custom indicator can help you forecast potential price movements with greater accuracy, using historical data.
Introduction
Predicting future price movements is always a challenge for traders and investors. However, by using historical data and statistical analysis, it is possible to make educated guesses about the likelihood of certain outcomes. One such tool for predicting future prices is the Price Extrapolator with Standard Deviation Cones. This custom indicator, can help you visualize potential price movements and their associated risks.
In this post, we will explain how the Price Extrapolator with Deviation Cones works, how to adjust its settings to suit your needs, and how to interpret its output. By the end of this article, you should have a better understanding of how this powerful tool can help you make more informed decisions when trading or investing in financial markets.
Understanding the Price Extrapolator with Deviation Cones
The Price Extrapolator with Deviation Cones is a custom indicator that uses historical price data to calculate the average log return and standard deviation of log returns over a specified period. It then uses this information to extrapolate a series of future price points, as well as upper and lower standard deviation bands that form the "deviation cones."
The average log return represents the expected price change, while the standard deviation of log returns provides a measure of the uncertainty or risk associated with the prediction. The deviation cones can help you visualize the range of potential price movements and assess the likelihood of different outcomes.
Configuring the Indicator
To use the Price Extrapolator with Deviation Cones, you will need to configure several input settings:
1. Length: This setting determines the number of historical data points used to calculate the average log return and standard deviation of log returns. A higher value will produce a smoother, less sensitive indicator, while a lower value will make the indicator more responsive to recent price changes.
2. Number of Future Price Points: This setting controls the number of future price points to extrapolate. Increasing this value will extend the deviation cones further into the future.
3. Multiplier: This setting adjusts the tightness of the deviation cones by controlling the standard deviation multiplier. A higher value will result in wider cones, indicating greater uncertainty, while a lower value will produce narrower cones, suggesting more confidence in the prediction.
Interpreting the Output
After configuring the indicator, you will see the following output on your chart:
1. Green Line: This line represents the extrapolated future price points based on the average log return. It provides a central estimate of potential price movements.
2. Red Lines: These lines form the upper and lower bounds of the deviation cones. They represent the range of potential price movements, taking into account the uncertainty associated with the prediction.
When using the Price Extrapolator with Deviation Cones, it is essential to remember that the output is only a prediction based on historical data and should not be taken as a guarantee of future price movements. However, by providing a visual representation of potential price movements and their associated risks, this indicator can help you make more informed decisions when trading or investing in financial markets.
The Extreme Limitations of the Price Extrapolator with Deviation Cones
While the Price Extrapolator with Deviation Cones can be a valuable addition to your trading toolbox, it is essential to recognize its limitations. As with any forecasting tool, it is not infallible and should be used in conjunction with other forms of analysis. In this section, we will discuss the extreme limitations of this indicator and provide insight into how to use it effectively despite these constraints.
1. Reliance on Historical Data
The Price Extrapolator with Deviation Cones relies heavily on historical price data to make its predictions. While this can provide valuable insights into past trends and patterns, it may not accurately predict future price movements in a constantly changing market.
Market conditions can change rapidly, and historical data may not be a reliable indicator of future performance. Economic events, geopolitical tensions, and changes in market sentiment can all influence price movements in ways that may not be captured by historical data alone.
2. Assumption of Lognormal Distribution
The indicator assumes that price returns follow a lognormal distribution, which may not always be the case. Financial markets can exhibit skewness and kurtosis, resulting in distributions that are not symmetrical or normally distributed. This can lead to inaccurate predictions and a false sense of security when relying on the deviation cones.
3. No Consideration of Fundamental Factors
The Price Extrapolator with Deviation Cones is a purely technical analysis tool, meaning it does not take into account fundamental factors that can influence price movements. Changes in company earnings, interest rates, or economic data can significantly impact asset prices and may not be factored into the indicator's predictions.
4. Limited Time Horizon
The indicator only provides predictions for a limited number of future price points, which may not be sufficient for long-term investors or traders with longer holding periods. Additionally, the accuracy of the predictions may decrease as the time horizon extends, due to the compounding effects of uncertainty and the limitations of historical data.
5. Potential for Overfitting
When adjusting the settings of the Price Extrapolator with Deviation Cones, there is a risk of overfitting the model to the historical data. This can result in an indicator that appears to have excellent predictive power on past data but performs poorly on unseen, future data. It is crucial to be cautious when optimizing the settings and use out-of-sample testing to validate the indicator's performance.
Using the Price Extrapolator with Deviation Cones Effectively
Despite these limitations, the Price Extrapolator with Deviation Cones can still be a valuable tool when used correctly. To use this indicator effectively, consider the following tips:
1. Supplement with Other Forms of Analysis: Use the Price Extrapolator with Deviation Cones alongside other technical and fundamental analysis methods to gain a more comprehensive understanding of potential price movements.
2. Diversify your Trading Strategies: Do not rely solely on the Price Extrapolator with Deviation Cones for your trading decisions. Instead, diversify your strategies and consider multiple indicators and methods to reduce the risk of overreliance on a single tool.
3. Be Cautious with Optimized Settings: When adjusting the indicator's settings, be mindful of the risk of overfitting and validate the performance with out-of-sample testing.
4. Keep an Eye on Market Conditions: Stay informed about current market conditions, economic events, and news that may impact your trading decisions. This will help you make more informed decisions when using the Price Extrapolator with Deviation Cones.
In conclusion, the Price Extrapolator with Deviation Cones is a powerful and versatile tool that can aid traders and investors in predicting potential future price movements. However, it is crucial to remember that this indicator has its limitations, which stem from its reliance on historical data, the assumption of lognormal distribution, its disregard for fundamental factors, limited time horizons, and the potential for overfitting. Despite these constraints, when used correctly and in conjunction with other forms of analysis, the Price Extrapolator with Deviation Cones can provide valuable insights and assist in making more informed trading and investing decisions.
By understanding the underlying mechanics of the indicator, adjusting its settings according to your needs, and being aware of its limitations, you can incorporate the Price Extrapolator with Deviation Cones into your trading arsenal effectively. Always remember that no single tool or indicator is infallible, and it is essential to use a diverse range of analysis methods and strategies to navigate the ever-changing financial markets successfully. Happy trading!
4 Pole ButterworthTitle: 4 Pole Butterworth Filter: A Smooth Filtering Technique for Technical Analysis
Introduction:
In technical analysis, filtering techniques are employed to remove noise from time-series data, helping traders to identify trends and make better-informed decisions. One such filtering technique is the 4 Pole Butterworth Filter. In this post, we will delve into the 4 Pole Butterworth Filter, explore its properties, and discuss its implementation in Pine Script for TradingView.
4 Pole Butterworth Filter:
The Butterworth filter is a type of infinite impulse response (IIR) filter that is widely used in signal processing applications. Named after the British engineer Stephen Butterworth, this filter is designed to have a maximally flat frequency response in the passband, meaning it does not introduce any distortions or ripples in the filtered signal.
The 4 Pole Butterworth Filter is a specific type of Butterworth filter that utilizes four poles in its transfer function. This design provides a steeper roll-off between the passband and the stopband, allowing for better noise reduction without significantly affecting the underlying data.
Why Choose the 4 Pole Butterworth Filter for Smoothing?
The 4 Pole Butterworth Filter is an excellent choice for smoothing in technical analysis due to its maximally flat frequency response in the passband. This property ensures that the filtered signal remains as close as possible to the original data, without introducing any distortions or ripples. Additionally, the 4 Pole Butterworth Filter provides a steeper roll-off between the passband and the stopband, enabling better noise reduction while preserving the essential features of the data.
Implementing the 4 Pole Butterworth Filter:
In Pine Script, we can implement the 4 Pole Butterworth Filter using a custom function called `fourpolebutter`. The function takes two input parameters: the source data (src) and the filter length (len). The filter length determines the cutoff frequency of the filter, which in turn affects the amount of smoothing applied to the data.
Within the `fourpolebutter` function, we first calculate the filter coefficients based on the filter length. These coefficients are essential for calculating the output of the filter at each data point. Next, we compute the filtered output using a recursive formula that involves the current and previous data points as well as the filter coefficients.
Finally, we create a script that takes user inputs for the source data and filter length and plots the 4 Pole Butterworth Filter on a TradingView chart.
By adjusting the input parameters, users can configure the 4 Pole Butterworth Filter to suit their specific requirements and improve the readability of their charts.
Conclusion:
The 4 Pole Butterworth Filter is a powerful smoothing technique that can be used in technical analysis to effectively reduce noise in time-series data. Its maximally flat frequency response in the passband ensures that the filtered signal remains as close as possible to the original data, while its steeper roll-off between the passband and the stopband provides better noise reduction. By implementing this filter in Pine Script, traders can easily integrate it into their trading strategies and enhance the clarity of their charts.
Chebyshev type I and II FilterTitle: Chebyshev Type I and II Filters: Smoothing Techniques for Technical Analysis
Introduction:
In technical analysis, smoothing techniques are used to remove noise from a time series data. They help to identify trends and improve the readability of charts. One such powerful smoothing technique is the Chebyshev Type I and II Filters. In this post, we will dive deep into the Chebyshev filters, discuss their significance, and explain the differences between Type I and Type II filters.
Chebyshev Filters:
Chebyshev filters are a class of infinite impulse response (IIR) filters that are widely used in signal processing applications. They are known for their ability to provide a sharper cutoff between the passband and the stopband compared to other filter types, such as Butterworth filters. The Chebyshev filters are named after the Russian mathematician Pafnuty Chebyshev, who created the Chebyshev polynomials that form the basis for these filters.
The two main types of Chebyshev filters are:
1. Chebyshev Type I filters: These filters have an equiripple passband, which means they have equal and constant ripple within the passband. The advantage of Type I filters is that they usually provide a faster roll-off rate between the passband and the stopband compared to other filter types. However, the trade-off is that they may have larger ripples in the passband, resulting in a less smooth output.
2. Chebyshev Type II filters: These filters have an equiripple stopband, which means they have equal and constant ripple within the stopband. The advantage of Type II filters is that they provide a more controlled output by minimizing the ripple in the passband. However, this comes at the cost of a slower roll-off rate between the passband and the stopband compared to Type I filters.
Why Choose Chebyshev Filters for Smoothing?
Chebyshev filters are an excellent choice for smoothing in technical analysis due to their ability to provide a sharper transition between the passband and the stopband. This sharper transition helps in preserving the essential features of the underlying data while effectively removing noise. The two types of Chebyshev filters offer different trade-offs between the smoothness of the output and the roll-off rate, allowing users to choose the one that best suits their requirements.
Implementing Chebyshev Filters:
In the Pine Script language, we can implement the Chebyshev Type I and II filters using custom functions. We first define the custom hyperbolic functions cosh, acosh, sinh, and asinh, as well as the inverse tangent function atan. These functions are essential for calculating the filter coefficients.
Next, we create two separate functions for the Chebyshev Type I and II filters, named chebyshevI and chebyshevII, respectively. Each function takes three input parameters: the source data (src), the filter length (len), and the ripple value (ripple). The ripple value determines the amount of ripple in the passband for Type I filters and in the stopband for Type II filters. A higher ripple value results in a faster roll-off rate but may lead to a less smooth output.
Finally, we create a main function called chebyshev, which takes an additional boolean input parameter named style. If the style parameter is set to false, the function calculates the Chebyshev Type I filter using the chebyshevI function. If the style parameter is set to true, the function calculates the Chebyshev Type II filter using the chebyshevII function.
By adjusting the input parameters, users can choose the type of Chebyshev filter and configure its characteristics to suit their needs.
Conclusion:
The Chebyshev Type I and II filters are powerful smoothing techniques that can be used in technical analysis to remove noise from time series data. They offer a sharper transition between the passband and the stopband compared to other filter types, which helps in preserving the essential features of the data while effectively reducing noise. By implementing these filters in Pine Script, traders can easily integrate them into their trading strategies and improve the readability of their charts.
Uptrend Downtrend Loopback Candle Identification LibThis library is for identifying uptrends and downtrends using a loopback candle analysis method. Which contains two functions:
uptrendLoopbackCandleIdentification() and downtrendLoopbackCandleIdentification() . These functions check if the current candle is part of an uptrend or downtrend, respectively, based on the specified lookback period.
The uptrendLoopbackCandleIdentification() takes two arguments: index , which is the index of the current bar, and lookbackPeriod , which is the number of previous candles to check for an uptrend. The function returns false if the index is less than the lookback period. Otherwise, it initializes a boolean variable isHigherHigh as true and loops through the previous candles. If any of the previous candles have a higher high than the current candle, isHigherHigh is set to false , and the loop breaks. Finally, the function returns the value of isHigherHigh .
The downtrendLoopbackCandleIdentification() takes the same arguments and returns false if the index is less than the lookback period. The function initializes a boolean variable isHigherLow as true and loops through the previous candles. If any of the previous candles have a higher low than the current candle, isHigherLow is set to false , and the loop breaks. The function returns the value of isHigherLow .
Goertzel Cycle Composite Wave [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Cycle Composite Wave indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
*** To decrease the load time of this indicator, only XX many bars back will render to the chart. You can control this value with the setting "Number of Bars to Render". This doesn't have anything to do with repainting or the indicator being endpointed***
█ Brief Overview of the Goertzel Cycle Composite Wave
The Goertzel Cycle Composite Wave is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The Goertzel Cycle Composite Wave is considered a non-repainting and endpointed indicator. This means that once a value has been calculated for a specific bar, that value will not change in subsequent bars, and the indicator is designed to have a clear start and end point. This is an important characteristic for indicators used in technical analysis, as it allows traders to make informed decisions based on historical data without the risk of hindsight bias or future changes in the indicator's values. This means traders can use this indicator trading purposes.
The repainting version of this indicator with forecasting, cycle selection/elimination options, and data output table can be found here:
Goertzel Browser
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the cycles. The color of the lines indicates whether the wave is increasing or decreasing.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast: These inputs define the window size for the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Cycle Composite Wave Code
The Goertzel Cycle Composite Wave code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Cycle Composite Wave function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past sizes (WindowSizePast), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Cycle Composite Wave algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Cycle Composite Wave code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Cycle Composite Wave code calculates the waveform of the significant cycles for specified time windows. The windows are defined by the WindowSizePast parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in a matrix:
The calculated waveforms for the cycle is stored in the matrix - goeWorkPast. This matrix holds the waveforms for the specified time windows. Each row in the matrix represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Cycle Composite Wave function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Cycle Composite Wave code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Cycle Composite Wave's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for specified time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast:
The WindowSizePast is updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
The matrix goeWorkPast is initialized to store the Goertzel results for specified time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for waveforms:
The goertzel array is initialized to store the endpoint Goertzel.
Calculating composite waveform (goertzel array):
The composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Drawing composite waveform (pvlines):
The composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms and visualizes them on the chart using colored lines.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
Limited applicability:
The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Cycle Composite Wave indicator can be interpreted by analyzing the plotted lines. The indicator plots two lines: composite waves. The composite wave represents the composite wave of the price data.
The composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend.
Interpreting the Goertzel Cycle Composite Wave indicator involves identifying the trend of the composite wave lines and matching them with the corresponding bullish or bearish color.
█ Conclusion
The Goertzel Cycle Composite Wave indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Cycle Composite Wave indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Cycle Composite Wave indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
Adaptive Price Channel StrategyThis strategy is an adaptive price channel strategy based on the Average True Range (ATR) indicator and the Average Directional Index (ADX). It aims to identify sideways markets and trends in the price movements and make trades accordingly.
The strategy uses a length parameter for the ATR and ADX indicators, which determines the length of the calculation for these indicators. The strategy also uses an ATR multiplier, which is multiplied by the ATR to determine the upper and lower bounds of the price channel.
The first step of the strategy is to calculate the highest high (HH) and lowest low (LL) over the specified length. The ATR is also calculated over the same length. Then the strategy calculates the positive directional indicator (+DI) and negative directional indicator (-DI) based on the up and down moves in the price, and uses these to calculate the ADX.
If the ADX is less than 25, the market is considered to be in a sideways phase. In this case, if the price closes above the upper bound of the price channel (HH - ATR multiplier * ATR), the strategy enters a long position, and if the price closes below the lower bound of the price channel (LL + ATR multiplier * ATR), the strategy enters a short position.
If the ADX is greater than or equal to 25 and the +DI is greater than the -DI, the market is considered to be in a bullish phase. In this case, if the price closes above the upper bound of the price channel, the strategy enters a long position. If the ADX is greater than or equal to 25 and the +DI is less than the -DI, the market is considered to be in a bearish phase. In this case, if the price closes below the lower bound of the price channel, the strategy enters a short position.
The strategy exits a position after a certain number of bars have passed since the entry, as specified by the exit_length input.
In summary, this strategy attempts to trade in accordance with the prevailing market conditions by identifying sideways markets and trends and making trades based on price movements within a dynamically-adjusted price channel.
This strategy takes a read on the market and either takes a channel strategy or trades volatility based on current trend. Works well on 2, 3 ,4, 12 hour for BTC. It’s my first attempt and creating a strategy. I am very interested in constructive criticism. I will look into better risk management, maybe a trailing stop loss. Other suggestions welcome. This is my first attempt at a strategy.
Here are the settings I used.
Inputs
Length 20
Exit 10
ATR 3.2
Dates I picked when I got into Crypto
Properties
Capital 1000
Order size 2 Contracts
Pyramiding 1
Commission .05
Goertzel Browser [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Browser indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
█ Brief Overview of the Goertzel Browser
The Goertzel Browser is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
3. Project the composite wave into the future, providing a potential roadmap for upcoming price movements.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the past and dotted lines for the future projections. The color of the lines indicates whether the wave is increasing or decreasing.
5. Displaying cycle information: The indicator provides a table that displays detailed information about the detected cycles, including their rank, period, Bartel's test results, amplitude, and phase.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements and their potential future trajectory, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast and WindowSizeFuture: These inputs define the window size for past and future projections of the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
UseCycleList: This boolean input determines whether a user-defined list of cycles should be used for constructing the composite wave. If set to false, the top N cycles will be used.
Cycle1, Cycle2, Cycle3, Cycle4, and Cycle5: These inputs define the user-defined list of cycles when 'UseCycleList' is set to true. If using a user-defined list, each of these inputs represents the period of a specific cycle to include in the composite wave.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Browser Code
The Goertzel Browser code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Browser function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past and future window sizes (WindowSizePast, WindowSizeFuture), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, goeWorkFuture, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Browser algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Browser code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Browser code calculates the waveform of the significant cycles for both past and future time windows. The past and future windows are defined by the WindowSizePast and WindowSizeFuture parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in matrices:
The calculated waveforms for each cycle are stored in two matrices - goeWorkPast and goeWorkFuture. These matrices hold the waveforms for the past and future time windows, respectively. Each row in the matrices represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Browser function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Browser code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Browser's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for both past and future time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast and WindowSizeFuture:
The WindowSizePast and WindowSizeFuture are updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
Two matrices, goeWorkPast and goeWorkFuture, are initialized to store the Goertzel results for past and future time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for past and future waveforms:
Three arrays, epgoertzel, goertzel, and goertzelFuture, are initialized to store the endpoint Goertzel, non-endpoint Goertzel, and future Goertzel projections, respectively.
Calculating composite waveform for past bars (goertzel array):
The past composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Calculating composite waveform for future bars (goertzelFuture array):
The future composite waveform is calculated in a similar way as the past composite waveform.
Drawing past composite waveform (pvlines):
The past composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
Drawing future composite waveform (fvlines):
The future composite waveform is drawn on the chart using dotted lines. The color of the lines is determined by the direction of the waveform (fuchsia for upward, yellow for downward).
Displaying cycle information in a table (table3):
A table is created to display the cycle information, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
Filling the table with cycle information:
The indicator iterates through the detected cycles and retrieves the relevant information (period, amplitude, phase, and Bartel value) from the corresponding arrays. It then fills the table with this information, displaying the values up to six decimal places.
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms for both past and future time windows and visualizes them on the chart using colored lines. Additionally, it displays detailed cycle information in a table, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles and potential future impact. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
No guarantee of future performance: While the script can provide insights into past cycles and potential future trends, it is important to remember that past performance does not guarantee future results. Market conditions can change, and relying solely on the script's predictions without considering other factors may lead to poor trading decisions.
Limited applicability: The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Browser indicator can be interpreted by analyzing the plotted lines and the table presented alongside them. The indicator plots two lines: past and future composite waves. The past composite wave represents the composite wave of the past price data, and the future composite wave represents the projected composite wave for the next period.
The past composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend. On the other hand, the future composite wave line is a dotted line with fuchsia indicating a bullish trend and yellow indicating a bearish trend.
The table presented alongside the indicator shows the top cycles with their corresponding rank, period, Bartels, amplitude or cycle strength, and phase. The amplitude is a measure of the strength of the cycle, while the phase is the position of the cycle within the data series.
Interpreting the Goertzel Browser indicator involves identifying the trend of the past and future composite wave lines and matching them with the corresponding bullish or bearish color. Additionally, traders can identify the top cycles with the highest amplitude or cycle strength and utilize them in conjunction with other technical indicators and fundamental analysis for trading decisions.
This indicator is considered a repainting indicator because the value of the indicator is calculated based on the past price data. As new price data becomes available, the indicator's value is recalculated, potentially causing the indicator's past values to change. This can create a false impression of the indicator's performance, as it may appear to have provided a profitable trading signal in the past when, in fact, that signal did not exist at the time.
The Goertzel indicator is also non-endpointed, meaning that it is not calculated up to the current bar or candle. Instead, it uses a fixed amount of historical data to calculate its values, which can make it difficult to use for real-time trading decisions. For example, if the indicator uses 100 bars of historical data to make its calculations, it cannot provide a signal until the current bar has closed and become part of the historical data. This can result in missed trading opportunities or delayed signals.
█ Conclusion
The Goertzel Browser indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Browser indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Browser indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
The first term represents the deviation of the data from the trend.
The second term represents the smoothness of the trend.
λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
Ticker Correlation Reference IndicatorHello,
I am super excited to be releasing this Ticker Correlation assessment indicator. This is a big one so let us get right into it!
Inspiration:
The inspiration for this indicator came from a similar indicator by Balipour called the Correlation with P-Value and Confidence Interval. It’s a great indicator, you should check it out!
I used it quite a lot when looking for correlations; however, there were some limitations to this indicator’s functionality that I wanted. So I decided to make my own indicator that had the functionality I wanted. I have been using this for some time but decided to actual spruce it up a bit and make it user friendly so that I could share it publically. So let me get into what this indicator does and, most importantly, the expanded functionality of this indicator.
What it does:
This indicator determines the correlation between 2 separate tickers. The user selects the two tickers they wish to compare and it performs a correlation assessment over a defaulted 14 period length and displays the results. However, the indicator takes this much further. The complete functionality of this indicator includes the following:
1. Assesses the correlation of all 4 ticker variables (Open, High, Low and Close) over a user defined period of time (defaulted to 14);
2. Converts both tickers to a Z-Score in order to standardize the data and provide a side by side comparison;
3. Displays areas of high and low correlation between all 4 variables;
4. Looks back over the consistency of the relationship (is correlation consistent among the two tickers or infrequent?);
5. Displays the variance in the correlation (there may be a statistically significant relationship, but if there is a high variance, it means the relationship is unstable);
6. Permits manual conversion between prices; and
7. Determines the degree of statistical significance (be it stable, unstable or non-existent).
I will discuss each of these functions below.
Function 1: Assesses the correlation of all 4 variables.
The only other indicator that does this only determines the correlation of the close price. However, correlation between all 4 variables varies. The correlation between open prices, high prices, low prices and close prices varies in statistically significant ways. As such, this indicator plots the correlation of all 4 ticker variables and displays each correlation.
Assessing this matters because sometimes a stock may not have the same magnitude in highs and lows as another stock (one stock may be more bullish, i.e. attain higher highs in comparison to another stock). Close price is helpful but does not pain the full picture. As such, the indicator displays the correlation relationship between all 4 variables (image below):
Function 2: Converts both tickers to Z-Score
Z-Score is a way of standardizing data. It simply measures how far a stock is trading in relation to its mean. As such, it is a way to express both tickers on a level playing field. Z-Score was also chosen because the Z-Score Values (0 – 4) also provide an appropriate scale to plot correlation lines (which range from 0 to 1).
The primary ticker (Ticker 1) is plotted in blue, the secondary comparison ticker (Ticker 2) is plotted in a colour changing format (which will be discussed below). See the image below:
Function 3: Displays areas of high and low correlation
While Ticker 1 is plotted in a static blue, Ticker 2 (the comparison ticker) is plotted in a dynamic, colour changing format. It will display areas of high correlation (i.e. areas with a P value greater than or equal to 0.9 or less than and equal to -0.9) in green, areas of moderate correlation in white. Areas of low correlation (between 0.4 and 0 or -0.4 and 0) are in red. (see image below):
Function 4: Checks consistency of relationship
While at the time of assessing a stock there very well maybe a high correlation, whether that correlation is consistent or not is the question. The indicator employs the use of the SMA function to plot the average correlation over a defined period of time. If the correlation is consistently high, the SMA should be within an area of statistical significance (over 0.5 or under -0.5). If the relationship is inconsistent, the SMA will read a lower value than the actual correlation.
You can see an example of this when you compare ETH to Tezos in the image below:
You can see that the correlation between ETH and Tezo’s on the high level seems to be inconsistent. While the current correlation is significant, the SMA is showing that the average correlation between the highs is actually less than 0.5.
The indicator also tells the user narratively the degree of consistency in the statistical relationship. This will be discussed later.
Function 5: Displays the variance
When it comes to correlation, variance is important. Variance simply means the distance between the highest and lowest value. The indicator assess the variance. A high degree of variance (i.e. a number surpassing 0.5 or greater) generally means the consistency and stability of the relationship is in issue. If there is a high variance, it means that the two tickers, while seemingly significantly correlated, tend to deviate from each other quite extensively.
The indicator will tell the user the variance in the narrative bar at the bottom of the chart (see image below):
Function 6: Permits manual conversion of price
One thing that I frequently want and like to do is convert prices between tickers. If I am looking at SPX and I want to calculate a price on SPY, I want to be able to do that quickly. This indicator permits you to do that by employing a regression based formula to convert Ticker 1 to Ticker 2.
The user can actually input which variable they would like to convert, whether they want to convert Ticker 1 Close to Ticker 2 Close, or Ticker 1 High to Ticker 2 High, or low or open.
To do this, open the settings and click “Permit Manual Conversion”. This will then take the current Ticker 1 Close price and convert it to Ticker 2 based on the regression calculations.
If you want to know what a specific price on Ticker 1 is on Ticker 2, simply click the “Allow Manual Price Input” variable and type in the price of Ticker 1 you want to know on Ticker 2. It will perform the calculation for you and will also list the standard error of the calculation.
Below is an example of calculating a SPY price using SPX data:
Above, the indicator was asked to convert an SPX price of 4,100 to a SPY price. The result was 408.83 with a standard error of 4.31, meaning we can expect 4,100 to fall within 408.83 +/- 4.31 on SPY.
Function 7: Determines the degree of statistical significance
The indicator will provide the user with a narrative output of the degree of statistical significance. The indicator looks beyond simply what the correlation is at the time of the assessment. It uses the SMA and the highest and lowest function to make an assessment of the stability of the statistical relationship and then indicates this to the user. Below is an example of IWM compared to SPY:
You will see, the indicator indicates that, while there is a statistically significant positive relationship, the relationship is somewhat unstable and inconsistent. Not only does it tell you this, but it indicates the degree of inconsistencies by listing the variance and the range of the inconsistencies.
And below is SPY to DIA:
SPY to BTCUSD:
And finally SPY to USDCAD Currency:
Other functions:
The indicator will also plot the raw or smoothed correlation result for the Open, High, Low or Close price. The default is to close price and smoothed. Smoothed just means it is displaying the SMA over the raw correlation score. Unsmoothing it will show you the raw correlation score.
The user also has the ability to toggle on and off the correlation table and the narrative table so that they can just review the chart (the side by side comparison of the 2 tickers).
Customizability
All of the functions are customizable for the most part. The user can determine the length of lookback, etc. The default parameters for all are 14. The only thing not customizable is the assessment used for determining the stability of a statistical relationship (set at 100 candle lookback) and the regression analysis used to convert price (10 candle lookback).
User Notes and important application tips:
#1: If using the manual calculation function to convert price, it is recommended to use this on the hourly or daily chart.
#2: Leaving pre-market data on can cause some errors. It is recommended to use the indicator with regular market hours enabled and extended market hours disabled.
#3: No ticker is off limits. You can compare anything against anything! Have fun with it and experiment!
Non-Indicator Specific Discussions:
Why does correlation between stocks mater?
This can matter for a number of reasons. For investors, it is good to diversify your portfolio and have a good array of stocks that operate somewhat independently of each other. This will allow you to see how your investments compare to each other and the degree of the relationship.
Another function may be getting exposure to more expensive tickers. I am guilty of trading IWM to gain exposure to SPY at a reduced cost basis :-).
What is a statistically significant correlation?
The rule of thumb is anything 0.5 or greater is considered statistically significant. The ideal setup is 0.9 or more as the effect is almost identical. That said, a lot of factors play into statistical significance. For example, the consistency and variance are 2 important factors most do not consider when ascertaining significance. Perhaps IWM and SPY are significantly correlated today, but is that a reliable relationship and can that be counted on as a rule?
These are things that should be considered when trading one ticker against another and these are things that I have attempted to address with this indicator!
Final notes:
I know I usually do tutorial videos. I have not done one here, but I will. Check back later for this.
I hope you enjoy the indicator and please feel free to share your thoughts and suggestions!
Safe trades all!
