Adaptive Quadratic Kernel EnvelopeThis study draws a fair-value curve from a quadratic-weighted (Nadaraya-Watson) regression. Alpha sets how sharply weights decay inside the look-back window, so you trade lag against smoothness with one slider. Band half-width is ATRslow times a bounded fast/slow ATR ratio, giving an instant response to regime shifts without overshooting on spikes. Work in log space when an instrument grows exponentially, equal percentage moves then map to equal vertical steps. NearBase and FarBase define a progression of adaptive thresholds, useful for sizing exits or calibrating mean-reversion logic. Non-repaint mode keeps one-bar delay for clean back-tests, predictive mode shows the zero-lag curve for live decisions.
Key points
- Quadratic weights cut phase error versus Gaussian or SMA-based envelopes.
- Dual-ATR scaling updates width on the next bar, no residual lag.
- Log option preserves envelope symmetry across multi-decade data.
- Alpha provides direct control of curvature versus noise.
- Built-in alerts trigger on the first adaptive threshold, ready for automation.
Typical uses
Trend bias from the slope of the curve.
Entry timing when price pierces an inner threshold and momentum stalls.
Breakout confirmation when closes hold beyond outer thresholds while volatility expands.
Stops and targets anchored to chosen thresholds, automatically matching current noise.
Kernel
Half Causal EstimatorOverview
The Half Causal Estimator is a specialized filtering method that provides responsive averages of market variables (volume, true range, or price change) with significantly reduced time delay compared to traditional moving averages. It employs a hybrid approach that leverages both historical data and time-of-day patterns to create a timely representation of market activity while maintaining smooth output.
Core Concept
Traditional moving averages suffer from time lag, which can delay signals and reduce their effectiveness for real-time decision making. The Half Causal Estimator addresses this limitation by using a non-causal filtering method that incorporates recent historical data (the causal component) alongside expected future behavior based on time-of-day patterns (the non-causal component).
This dual approach allows the filter to respond more quickly to changing market conditions while maintaining smoothness. The name "Half Causal" refers to this hybrid methodology—half of the data window comes from actual historical observations, while the other half is derived from time-of-day patterns observed over multiple days. By incorporating these "future" values from past patterns, the estimator can reduce the inherent lag present in traditional moving averages.
How It Works
The indicator operates through several coordinated steps. First, it stores and organizes market data by specific times of day (minutes/hours). Then it builds a profile of typical behavior for each time period. For calculations, it creates a filtering window where half consists of recent actual data and half consists of expected future values based on historical time-of-day patterns. Finally, it applies a kernel-based smoothing function to weight the values in this composite window.
This approach is particularly effective because market variables like volume, true range, and price changes tend to follow recognizable intraday patterns (they are positive values without DC components). By leveraging these patterns, the indicator doesn't try to predict future values in the traditional sense, but rather incorporates the average historical behavior at those future times into the current estimate.
The benefit of using this "average future data" approach is that it counteracts the lag inherent in traditional moving averages. In a standard moving average, recent price action is underweighted because older data points hold equal influence. By incorporating time-of-day averages for future periods, the Half Causal Estimator essentially shifts the center of the filter window closer to the current bar, resulting in more timely outputs while maintaining smoothing benefits.
Understanding Kernel Smoothing
At the heart of the Half Causal Estimator is kernel smoothing, a statistical technique that creates weighted averages where points closer to the center receive higher weights. This approach offers several advantages over simple moving averages. Unlike simple moving averages that weight all points equally, kernel smoothing applies a mathematically defined weight distribution. The weighting function helps minimize the impact of outliers and random fluctuations. Additionally, by adjusting the kernel width parameter, users can fine-tune the balance between responsiveness and smoothness.
The indicator supports three kernel types. The Gaussian kernel uses a bell-shaped distribution that weights central points heavily while still considering distant points. The Epanechnikov kernel employs a parabolic function that provides efficient noise reduction with a finite support range. The Triangular kernel applies a linear weighting that decreases uniformly from center to edges. These kernel functions provide the mathematical foundation for how the filter processes the combined window of past and "future" data points.
Applicable Data Sources
The indicator can be applied to three different data sources: volume (the trading volume of the security), true range (expressed as a percentage, measuring volatility), and change (the absolute percentage change from one closing price to the next).
Each of these variables shares the characteristic of being consistently positive and exhibiting cyclical intraday patterns, making them ideal candidates for this filtering approach.
Practical Applications
The Half Causal Estimator excels in scenarios where timely information is crucial. It helps in identifying volume climaxes or diminishing volume trends earlier than conventional indicators. It can detect changes in volatility patterns with reduced lag. The indicator is also useful for recognizing shifts in price momentum before they become obvious in price action, and providing smoother data for algorithmic trading systems that require reduced noise without sacrificing timeliness.
When volatility or volume spikes occur, conventional moving averages typically lag behind, potentially causing missed opportunities or delayed responses. The Half Causal Estimator produces signals that align more closely with actual market turns.
Technical Implementation
The implementation of the Half Causal Estimator involves several technical components working together. Data collection and organization is the first step—the indicator maintains a data structure that organizes market data by specific times of day. This creates a historical record of how volume, true range, or price change typically behaves at each minute/hour of the trading day.
For each calculation, the indicator constructs a composite window consisting of recent actual data points from the current session (the causal half) and historical averages for upcoming time periods from previous sessions (the non-causal half). The selected kernel function is then applied to this composite window, creating a weighted average where points closer to the center receive higher weights according to the mathematical properties of the chosen kernel. Finally, the kernel weights are normalized to ensure the output maintains proper scaling regardless of the kernel type or width parameter.
This framework enables the indicator to leverage the predictable time-of-day components in market data without trying to predict specific future values. Instead, it uses average historical patterns to reduce lag while maintaining the statistical benefits of smoothing techniques.
Configuration Options
The indicator provides several customization options. The data period setting determines the number of days of observations to store (0 uses all available data). Filter length controls the number of historical data points for the filter (total window size is length × 2 - 1). Filter width adjusts the width of the kernel function. Users can also select between Gaussian, Epanechnikov, and Triangular kernel functions, and customize visual settings such as colors and line width.
These parameters allow for fine-tuning the balance between responsiveness and smoothness based on individual trading preferences and the specific characteristics of the traded instrument.
Limitations
The indicator requires minute-based intraday timeframes, securities with volume data (when using volume as the source), and sufficient historical data to establish time-of-day patterns.
Conclusion
The Half Causal Estimator represents an innovative approach to technical analysis that addresses one of the fundamental limitations of traditional indicators: time lag. By incorporating time-of-day patterns into its calculations, it provides a more timely representation of market variables while maintaining the noise-reduction benefits of smoothing. This makes it a valuable tool for traders who need to make decisions based on real-time information about volume, volatility, or price changes.
Machine Learning SupertrendThe Machine Learning Supertrend is an advanced trend-following indicator that enhances the traditional Supertrend with Gaussian Process Regression (GPR) and kernel-based learning. Unlike conventional methods that rely purely on historical ATR values, this indicator integrates machine learning techniques to dynamically estimate volatility and forecast future price movements, resulting in a more adaptive and robust trend detection system.
At the core of this indicator lies Gaussian Process Regression (GPR), which utilizes a Radial Basis Function (RBF) kernel to model price distributions and anticipate future trends. Instead of simply looking at past price action, it constructs a kernel matrix, enabling a probabilistic approach to price forecasting. This allows the indicator to not only detect current trends but also project potential trend reversals with greater accuracy.
By applying machine learning to ATR estimation, the ML Supertrend dynamically adjusts its thresholds based on predicted values rather than a fixed multiplier. This makes the trend signals more responsive to market conditions, reducing false signals and minimizing whipsaws often seen with traditional Supertrend indicators. The upper and lower bands are no longer static but evolve based on the underlying price structure, improving the reliability of trend shifts.
When the price crosses these adaptive levels, the indicator detects a trend change and plots it accordingly. Green signifies a bullish trend, while red indicates a bearish one. Alerts can also be triggered when the trend shifts, allowing traders to react quickly to potential reversals.
What makes this approach powerful is its ability to adapt to different market conditions. Traditional ATR-based methods use fixed parameters that might not always be optimal, whereas this ML-driven Supertrend continuously refines its estimations based on real-time data. The result is a more intelligent, less lagging, and highly adaptive trend-following tool.
This indicator is particularly useful for traders looking to enhance trend-following strategies with AI-driven insights. It reduces noise, improves signal reliability, and even offers a degree of trend forecasting, making it ideal for those who want a more advanced and dynamic alternative to standard Supertrend indicators.
This indicator is provided for educational and informational purposes only. It does not constitute financial advice, and past performance is not indicative of future results. Trading involves risk, and users should conduct their own research and use proper risk management before making investment decisions.
Trend Regression Kernel [IkkeOmar]Kernel by @jdehorty huge shoutout to him! This is only an idea for how I use it when trading
All credit for the kernel goes to him, I did not make the kernel! I don't know how to make it more clear.
I use this to assist with top-down analysis.
timeframe I want to trade : timeframe to analyse with white noise and kernel:
1m : 1H
5m : 2H
15m : 4H
1H : 1D
In the chart you see that I have the 1H open, I use the white noise at a "lower setting length" (55 in this case), I change the source of to be the kernel on the higher timeframe. When a new trend is detected by the White noise I wait for price to retest the kernel before building a position. Another case described below:
Here i use the adaptive MCVF (I have made this free for everyone on TradingView) to buy when price is below the kernel while the trend for the white noise is bullish .
Notice that the Kernel is set on the 4H timeframe! The source of the white noise is the kernel!
Here is an example in a bearish trend:
Notice, I am on the 5m chart, kernel uses the 2H chart and the source of the white noise is the kernel.
I use the adaptive MCVF to help me get entries AFTER the first touch of the kernel.
Mandatory code explanation, with respect to the house rules:
Input settings:
Input Settings:
The script provides various input parameters to customize the indicator:
src: The source of price data, defaulted to closing prices.
h, r, x_0: Parameters for Kernel 1.
h2, r2, x_2: Parameters for Kernel 2.
Kernel Regression Functions:
Two functions kernel_regression1 and kernel_regression2 are defined to perform kernel regression calculations.
These functions estimate the trend using the Nadaraya-Watson kernel non-parametric regression method.
They take the source data (_src), the size of the data series (_size), and the lookback window (_h) as inputs.
They iterate over the data series and calculate the weighted sum of the values based on the specified kernel parameters.
The result is divided by the cumulative weight to obtain the estimated value.
Estimations:
The kernel_regression1 and kernel_regression2 functions are called with the respective parameters to estimate trends (yhat1 and yhat2).
Buy and Sell Signals:
Buy and sell signals are generated based on crossover and crossunder conditions between the two trend estimates (yhat1 and yhat2).
buySignal is true when yhat1 crosses above yhat2.
SellSignal is true when yhat1 crosses below yhat2.
Plotting:
The average of the two trend estimates (yhat1 and yhat2) is calculated and plotted.
The color of the plot is determined based on whether yhat1 is greater than yhat2, less than yhat2, or equal to yhat2.
Buy and sell signals are plotted using triangle shapes below and above bars, respectively.
Alerts:
Alert conditions are set based on buy and sell signals. Alerts are triggered when a crossover (long signal) or crossunder (short signal) occurs.
The alerts include information about the signal type, symbol, and price.
It's important to mention that the buy and sell signals from the indicator is very discretionary, I rarely use them, and if I do it's if they are in confluence with a correction i am biased towards or if it has confluence with some of my other systems.
The adaptive MCVF and White noise is free for everyone on TradingView, linked below:)
Huge shoutout to @jdehorty, original kernel below:
Kernels©2024, GoemonYae; copied from @jdehorty's "KernelFunctions" on 2024-03-09 to ensure future dependency compatibility. Will also add more functions to this script.
Library "KernelFunctions"
This library provides non-repainting kernel functions for Nadaraya-Watson estimator implementations. This allows for easy substition/comparison of different kernel functions for one another in indicators. Furthermore, kernels can easily be combined with other kernels to create newer, more customized kernels.
rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar)
Rational Quadratic Kernel - An infinite sum of Gaussian Kernels of different length scales.
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_relativeWeight (simple float) : Relative weighting of time frames. Smaller values resut in a more stretched out curve and larger values will result in a more wiggly curve. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel.
startAtBar (simple int)
Returns: yhat The estimated values according to the Rational Quadratic Kernel.
gaussian(_src, _lookback, startAtBar)
Gaussian Kernel - A weighted average of the source series. The weights are determined by the Radial Basis Function (RBF).
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
startAtBar (simple int)
Returns: yhat The estimated values according to the Gaussian Kernel.
periodic(_src, _lookback, _period, startAtBar)
Periodic Kernel - The periodic kernel (derived by David Mackay) allows one to model functions which repeat themselves exactly.
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period (simple int) : The distance between repititions of the function.
startAtBar (simple int)
Returns: yhat The estimated values according to the Periodic Kernel.
locallyPeriodic(_src, _lookback, _period, startAtBar)
Locally Periodic Kernel - The locally periodic kernel is a periodic function that slowly varies with time. It is the product of the Periodic Kernel and the Gaussian Kernel.
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period (simple int) : The distance between repititions of the function.
startAtBar (simple int)
Returns: yhat The estimated values according to the Locally Periodic Kernel.
Bandwidth Volatility - Silverman Rule of thumb EstimatorOverview
This indicator calculates volatility using the Rule of Thumb bandwidth estimator and incorporating the standard deviations of returns to get historical volatility. There are two options: one for the original rule of thumb bandwidth estimator, and another for the modified rule of thumb estimator. This indicator comes with the bandwidth , which is shown with the color gradient columns, which are colored by a percentile of the bandwidth, and the moving average of the bandwidth, which is the dark shaded area.
The rule of thumb bandwidth estimator is a simple and quick method for estimating the bandwidth parameter in kernel density estimation (KSE) or kernel regression. It provides a rough approximation of the bandwidth without requiring extensive computation resources or fine-tuning. One common rule of thumb estimator is Silverman rule, which is given by
h = 1.06*σ*n^(-1/5)
where
h is the bandwidth
σ is the standard deviation of the data
n is the number of data points
This rule of thumb is based on assuming a Gaussian kernel and aims to strike a balance between over-smoothing and under-smoothing the data. It is simple to implement and usually provides reasonable bandwidth estimates for a wide range of datasets. However , it is important to note that this rule of thumb may not always have optimal results, especially for non-Gaussian or multimodal distributions. In such cases, a modified bandwidth selection, such as cross-validation or even applying a log transformation (if the data is right-skewed), may be preferable.
How it works:
This indicator computes the bandwidth volatility using returns, which are used in the standard deviation calculation. It then estimates the bandwidth based on either the Silverman rule of thumb or a modified version considering the interquartile range. The percentile ranks of the bandwidth estimate are then used to visualize the volatility levels, identify high and low volatility periods, and show them with colors.
Modified Rule of thumb Bandwidth:
The modified rule of thumb bandwidth formula combines elements of standard deviations and interquartile ranges, scaled by a multiplier of 0.9 and inversely with a number of periods. This modification aims to provide a more robust and adaptable bandwidth estimation method, particularly suitable for financial time series data with potentially skewed or heavy-tailed data.
Formula for Modified Rule of Thumb Bandwidth:
h = 0.9 * min(σ, (IQR/1.34))*n^(-1/5)
This modification introduces the use of the IQR divided by 1.34 as an alternative to the standard deviation. It aims to improve the estimation, mainly when the underlying distribution deviates from a perfect Gaussian distribution.
Analysis
Rule of thumb Bandwidth: Provides a broader perspective on volatility trends, smoothing out short-term fluctuations and focusing more on the overall shape of the density function.
Historical Volatility: Offers a more granular view of volatility, capturing day-to-day or intra-period fluctuations in asset prices and returns.
Modelling Requirements
Rule of thumb Bandwidth: Provides a broader perspective on volatility trends, smoothing out short-term fluctuations and focusing more on the overall shape of the density function.
Historical Volatility: Offers a more granular view of volatility, capturing day-to-day or intra-period fluctuations in asset prices and returns.
Pros of Bandwidth as a volatility measure
Robust to Data Distribution: Bandwidth volatility, especially when estimated using robust methods like Silverman's rule of thumb or its modifications, can be less sensitive to outliers and non-normal distributions compared to some other measures of volatility
Flexibility: It can be applied to a wide range of data types and can adapt to different underlying data distributions, making it versatile for various analytical tasks.
How can traders use this indicator?
In finance, volatility is thought to be a mean-reverting process. So when volatility is at an extreme low, it is expected that a volatility expansion happens, which comes with bigger movements in price, and when volatility is at an extreme high, it is expected for volatility to eventually decrease, leading to smaller price moves, and many traders view this as an area to take profit in.
In the context of this indicator, low volatility is thought of as having the green color, which indicates a low percentile value, and also being below the moving average. High volatility is thought of as having the yellow color and possibly being above the moving average, showing that you can eventually expect volatility to decrease.
Kernel Regression RibbonKernel Regression Ribbon is a flexible, visually pleasing trend identification tool. Plotting 8 different kernel regressions of different types and parameters allows the user to see where levels of support and resistance are being tested, retested and broken.
What’s Kernel Regression?
A statistical method for estimating the best fitting curve for a dataset, in this case, a time/price chart.
How’s Kernel Regression different from a Moving Average?
A Moving Average is basically a simple form of Kernel Regression, in that it uses a fixed (Retangular) Kernel function. In an MA, all data points are weighted equally over its length. However, a Kernel function reacts more to data points that are closer to the current point. This means it will adapt more quickly to changes in data than an MA. Due to this adaptability, Kernel functions often form part of Machine Learning.
Using this indicator:
Explore the default Regular mode first to get a feel for the inputs, which are more numerous than for MAs. Try out different settings, filters and intervals to get the best out of each kernel. Not all parameters are available for each KR. There are info tips to explain this in the menu, but I’ve also included handy, optional labels on the chart for each KR as a more accessible guide.
Once you know your way round the Regular mode, check out the Presets and start changing the parameters of each kernel to your liking in the “User KR1, KR2, … “ mode. Each kernel type has its strong and weak points. Blending different kernels is where this indicator comes into its own. Give your charts a funky shine!
This indicator does NOT repaint.
This script acknowledges, and hopefully showcases, the great work of @veryfid Kernel Regression Toolkit.
Bollinger Bands (Nadaraya Smoothed) | Flux ChartsTicker: AMEX:SPY , Timeframe: 1m, Indicator settings: default
General Purpose
This script is an upgrade to the classic Bollinger Bands. The idea behind Bollinger bands is the detection of price movements outside of a stock's typical fluctuations. Bollinger Bands use a moving average over period n plus/minus the standard deviation over period n times a multiplier. When price closes above or below either band this can be considered an abnormal movement. This script allows for the classic Bollinger Band interpretation while de-noising or "smoothing" the bands.
Efficacy
Ticker: AMEX:SPY , Timeframe: 1m, Indicator settings: Standard Dev: 2; Level 1 : off; Level 2: off; labels: off
Upper Band Key:
Blue: Bollinger No smoothing
Orange: Bollinger SMA smoothing period of 10
Purple: Bollinger EMA smoothing period of 10
Red: Nadaraya Smoothed Bollinger bandwidth of 6
Here we chose periods so that each would have a similar offset from the original Bollinger's. Notice that the Red Band has a much smoother result while on average having a similar fit to the other smoothing techniques. Increasing the EMA's or SMA's period would result in them being smoother however the offset would increase making them less accurate to the original data.
Ticker: AMEX:SPY , Timeframe: 1m, Indicator settings: Standard Dev: 2; Level 1: off; Level 2: off; labels: off
Upper Band Key:
Blue: Bollinger No smoothing
Orange: Bollinger SMA smoothing period of 20
Purple: Bollinger EMA smoothing period of 20
Red: Nadaraya Smoothed Bollinger bandwidth of 6
This makes the Nadaraya estimator a particularly efficacious technique in this use case as it achieves a superior smoothness to fit ratio.
How to Use
This indicator is not intended to be used on its own. Its use case is to identify outlier movements and periods of consolidation. The Smoothing Factor when lowered results in a more reactive but noisy graph. This setting is also known as the "bandwidth" ; it essentially raises the amplitude of the kernel function causing a greater weighting to recent data similar to lowering the period of a SMA or EMA. The repaint smoothing simply draws on the Bollinger's each chart update. Typically repaint would be used for processing and displaying discrete data however currently it's simply another way to display the Bollinger Bands.
What makes this script unique.
Since Bollinger bands use standard deviation they have excess noise. By noise we mean minute fluctuations which most traders will not find useful in their strategies. The Nadaraya-Watson estimator, as used, is essentially a weighted average akin to an ema. A gaussian kernel is placed at the candlestick of interest. That candlestick's value will have the highest weight. From that point the other candlesticks' values effect on the average will decrease with the slope of the kernel function. This creates a localized mean of the Bollinger Bands allowing for reduced noise with minimal distortion of the original Bollinger data.
AI Momentum [YinYang]Overview:
AI Momentum is a kernel function based momentum Indicator. It uses Rational Quadratics to help smooth out the Moving Averages, this may give them a more accurate result. This Indicator has 2 main uses, first it displays ‘Zones’ that help you visualize the potential movement areas and when the price is out of bounds (Overvalued or Undervalued). Secondly it creates signals that display the momentum of the current trend.
The Zones are composed of the Highest Highs and Lowest lows turned into a Rational Quadratic over varying lengths. These create our Rational High and Low zones. There is however a second zone. The second zone is composed of the avg of the Inner High and Inner Low zones (yellow line) and the Rational Quadratic of the current Close. This helps to create a second zone that is within the High and Low bounds that may represent momentum changes within these zones. When the Rationalized Close crosses above the High and Low Zone Average it may signify a bullish momentum change and vice versa when it crosses below.
There are 3 different signals created to display momentum:
Bullish and Bearish Momentum. These signals display when there is current bullish or bearish momentum happening within the trend. When the momentum changes there will likely be a lull where there are neither Bullish or Bearish momentum signals. These signals may be useful to help visualize when the momentum has started and stopped for both the bulls and the bears. Bullish Momentum is calculated by checking if the Rational Quadratic Close > Rational Quadratic of the Highest OHLC4 smoothed over a VWMA. The Bearish Momentum is calculated by checking the opposite.
Overly Bullish and Bearish Momentum. These signals occur when the bar has Bullish or Bearish Momentum and also has an Rationalized RSI greater or less than a certain level. Bullish is >= 57 and Bearish is <= 43. There is also the option to ‘Factor Volume’ into these signals. This means, the Overly Bullish and Bearish Signals will only occur when the Rationalized Volume > VWMA Rationalized Volume as well as the previously mentioned factors above. This can be useful for removing ‘clutter’ as volume may dictate when these momentum changes will occur, but it can also remove some of the useful signals and you may miss the swing too if the volume just was low. Overly Bullish and Bearish Momentum may dictate when a momentum change will occur. Remember, they are OVERLY Bullish and Bearish, meaning there is a chance a correction may occur around these signals.
Bull and Bear Crosses. These signals occur when the Rationalized Close crosses the Gaussian Close that is 2 bars back. These signals may show when there is a strong change in momentum, but be careful as more often than not they’re predicting that the momentum may change in the opposite direction.
Tutorial:
As we can see in the example above, generally what happens is we get the regular Bullish or Bearish momentum, followed by the Rationalized Close crossing the Zone average and finally the Overly Bullish or Bearish signals. This is normally the order of operations but isn’t always how it happens as sometimes momentum changes don’t make it that far; also the Rationalized Close and Zone Average don’t follow any of the same math as the Signals which can result in differing appearances. The Bull and Bear Crosses are also quite sporadic in appearance and don’t generally follow any sort of order of operations. However, they may occur as a Predictor between Bullish and Bearish momentum, signifying the beginning of the momentum change.
The Bull and Bear crosses may be a Predictor of momentum change. They generally happen when there is no Bullish or Bearish momentum happening; and this helps to add strength to their prediction. When they occur during momentum (orange circle) there is a less likely chance that it will happen, and may instead signify the exact opposite; it may help predict a large spike in momentum in the direction of the Bullish or Bearish momentum. In the case of the orange circle, there is currently Bearish Momentum and therefore the Bull Cross may help predict a large momentum movement is about to occur in favor of the Bears.
We have disabled signals here to properly display and talk about the zones. As you can see, Rationalizing the Highest Highs and Lowest Lows over 2 different lengths creates inner and outer bounds that help to predict where parabolic movement and momentum may move to. Our Inner and Outer zones are great for seeing potential Support and Resistance locations.
The secondary zone, which can cross over and change from Green to Red is also a very important zone. Let's zoom in and talk about it specifically.
The Middle Zone Crosses may help deduce where parabolic movement and strong momentum changes may occur. Generally what may happen is when the cross occurs, you will see parabolic movement to the High / Low zones. This may be the Inner zone but can sometimes be the outer zone too. The hard part is sometimes it can be a Fakeout, like displayed with the Blue Circle. The Cross doesn’t mean it may move to the opposing side, sometimes it may just be predicting Parabolic movement in a general sense.
When we turn the Momentum Signals back on, we can see where the Fakeout occurred that it not only almost hit the Inner Low Zone but it also exhibited 2 Overly Bearish Signals. Remember, Overly bearish signals mean a momentum change in favor of the Bulls may occur soon and overly Bullish signals mean a momentum change in favor of the Bears may occur soon.
You may be wondering, well what does “may occur soon” mean and how do we tell?
The purpose of the momentum signals is not only to let you know when Momentum has occurred and when it is still prevalent. It also matters A LOT when it has STOPPED!
In this example above, we look at when the Overly Bullish and Bearish Momentum has STOPPED. As you can see, when the Overly Bullish or Bearish Momentum stopped may be a strong predictor of potential momentum change in the opposing direction.
We will conclude our Tutorial here, hopefully this Indicator has been helpful for showing you where momentum is occurring and help predict how far it may move. We have been dabbling with and are planning on releasing a Strategy based on this Indicator shortly.
Settings:
1. Momentum:
Show Signals: Sometimes it can be difficult to visualize the zones with signals enabled.
Factor Volume: Factor Volume only applies to Overly Bullish and Bearish Signals. It's when the Volume is > VWMA Volume over the Smoothing Length.
Zone Inside Length: The Zone Inside is the Inner zone of the High and Low. This is the length used to create it.
Zone Outside Length: The Zone Outside is the Outer zone of the High and Low. This is the length used to create it.
Smoothing length: Smoothing length is the length used to smooth out our Bullish and Bearish signals, along with our Overly Bullish and Overly Bearish Signals.
2. Kernel Settings:
Lookback Window: The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars. Recommended range: 3-50.
Relative Weighting: Relative weighting of time frames. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel. Recommended range: 0.25-25.
Start Regression at Bar: Bar index on which to start regression. The first bars of a chart are often highly volatile, and omission of these initial bars often leads to a better overall fit. Recommended range: 5-25.
If you have any questions, comments, ideas or concerns please don't hesitate to contact us.
HAPPY TRADING!
Relational Quadratic Kernel Channel [Vin]The Relational Quadratic Kernel Channel (RQK-Channel-V) is designed to provide more valuable potential price extremes or continuation points in the price trend.
Example:
Usage:
Lookback Window: Adjust the "Lookback Window" parameter to control the number of previous bars considered when calculating the Rational Quadratic Estimate. Longer windows capture longer-term trends, while shorter windows respond more quickly to price changes.
Relative Weight: The "Relative Weight" parameter allows you to control the importance of each data point in the calculation. Higher values emphasize recent data, while lower values give more weight to historical data.
Source: Choose the data source (e.g., close price) that you want to use for the kernel estimate.
ATR Length: Set the length of the Average True Range (ATR) used for channel width calculation. A longer ATR length results in wider channels, while a shorter length leads to narrower channels.
Channel Multipliers: Adjust the "Channel Multiplier" parameters to control the width of the channels. Higher multipliers result in wider channels, while lower multipliers produce narrower channels. The indicator provides three sets of channels, each with its own multiplier for flexibility.
Details:
Rational Quadratic Kernel Function:
The Rational Quadratic Kernel Function is a type of smoothing function used to estimate a continuous curve or line from discrete data points. It is often used in time series analysis to reduce noise and emphasize trends or patterns in the data.
The formula for the Rational Quadratic Kernel Function is generally defined as:
K(x) = (1 + (x^2) / (2 * α * β))^(-α)
Where:
x represents the distance or difference between data points.
α and β are parameters that control the shape of the kernel. These parameters can be adjusted to control the smoothness or flexibility of the kernel function.
In the context of this indicator, the Rational Quadratic Kernel Function is applied to a specified source (e.g., close prices) over a defined lookback window. It calculates a smoothed estimate of the source data, which is then used to determine the central value of the channels. The kernel function allows the indicator to adapt to different market conditions and reduce noise in the data.
The specific parameters (length and relativeWeight) in your indicator allows to fine-tune how the Rational Quadratic Kernel Function is applied, providing flexibility in capturing both short-term and long-term trends in the data.
To know more about unsupervised ML implementations, I highly recommend to follow the users, @jdehorty and @LuxAlgo
Optimizing the parameters:
Lookback Window (length): The lookback window determines how many previous bars are considered when calculating the kernel estimate.
For shorter-term trading strategies, you may want to use a shorter lookback window (e.g., 5-10).
For longer-term trading or investing, consider a longer lookback window (e.g., 20-50).
Relative Weight (relativeWeight): This parameter controls the importance of each data point in the calculation.
A higher relative weight (e.g., 2 or 3) emphasizes recent data, which can be suitable for trend-following strategies.
A lower relative weight (e.g., 1) gives more equal importance to historical and recent data, which may be useful for strategies that aim to capture both short-term and long-term trends.
ATR Length (atrLength): The length of the Average True Range (ATR) affects the width of the channels.
Longer ATR lengths result in wider channels, which may be suitable for capturing broader price movements.
Shorter ATR lengths result in narrower channels, which can be helpful for identifying smaller price swings.
Channel Multipliers (channelMultiplier1, channelMultiplier2, channelMultiplier3): These parameters determine the width of the channels relative to the ATR.
Adjust these multipliers based on your risk tolerance and desired channel width.
Higher multipliers result in wider channels, which may lead to fewer signals but potentially larger price movements.
Lower multipliers create narrower channels, which can result in more frequent signals but potentially smaller price movements.
Kernel Regression ToolkitThis toolkit provides filters and extra functionality for non-repainting Nadaraya-Watson estimator implementations made by @jdehorty. For the sake of ease I have nicknamed it "kreg". Filters include a smoothing formula and zero lag formula. The purpose of this script is to help traders test, experiment and develop different regression lines. Regression lines are best used as trend lines and can be an invaluable asset for quickly locating first pullbacks and breaks of trends.
Other features include two J lines and a blend line. J lines are featured in tools like Stochastic KDJ. The formula uses the distance between K and D lines to make the J line. The blend line adds the ability to blend two lines together. This can be useful for several tasks including finding a center/median line between two lines or for blending in the characteristics of a different line. Default is set to 50 which is a 50% blend of the two lines. This can be increased and decreased to taste. This tool can be overlaid on the chart or on top of another indicator if you set the source. It can even be moved into its own window to create a unique oscillator based on whatever sources you feed it.
Below are the standard settings for the kernel estimation as documented by @jdehorty:
Lookback Window: The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars. Recommended range: 3-50
Weighting: Relative weighting of time frames. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel. Recommended range: 0.25-25
Level: Bar index on which to start regression. Controls how tightly fit the kernel estimate is to the data. Smaller values are a tighter fit. Larger values are a looser fit. Recommended range: 2-25
Lag: Lag for crossover detection. Lower values result in earlier crossovers. Recommended range: 1-2
For more information on this technique refer to to the original open source indicator by @jdehorty located here:
KernelFunctionsFiltersLibrary "KernelFunctionsFilters"
This library provides filters for non-repainting kernel functions for Nadaraya-Watson estimator implementations made by @jdehorty. Filters include a smoothing formula and zero lag formula. You can find examples in the code. For more information check out the original library KernelFunctions.
rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_relativeWeight (simple float)
startAtBar (simple int)
_filter (simple string)
gaussian(_src, _lookback, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
startAtBar (simple int)
_filter (simple string)
periodic(_src, _lookback, _period, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_period (simple int)
startAtBar (simple int)
_filter (simple string)
locallyPeriodic(_src, _lookback, _period, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_period (simple int)
startAtBar (simple int)
_filter (simple string)
j(line1, line2)
Parameters:
line1 (float)
line2 (float)
Nadaraya-Watson OscillatorThis indicator is based on the work of @jdehorty and his amazing Nadaraya-Watson Kernel Envelope, which you can see here:
General Description
The Nadaraya-Watson Oscillator (NWO) will give the same information as the Nadaraya-Watson Envelope, but as an oscillator off the main chart, by plotting the relationship between price and the Kernel and its bands. This also means that we can now detect divergences between price and the NWO.
You can see the relationship between the two here:
You can think of this indicator as the kernel envelope version of a Bollinger Band %B. In ranging markets the bands are perfect for mean reversion trades, but in certain situations the break of one of the bands can signal the beggining of a strong trend and price will remain close to the bands for a long period and will only give small pullbacks. As with any indicator, confluence with price and other tools must be taken into account.
Main Features
As with @jdehorty 's Envelope, you can change the following settings:
Lookback Window.
Relative Weighting.
The initial bar for the regression.
ATR period for the bands.
Inner and Outer Multiples for the bands.
I also added the following:
A middle band around the Kernel to filter out false crossovers.
A Hull Moving Average to smoothen out the movements of the oscillator and give extra confirmation of turnover points.
Colors
Some special things to note regarding the coloring:
The zero line features a gradient that changes color every time the Kernel slope changes direction.
The Oscillator plot has a gradient coloring that gets stronger the closer it gets to each of the bands.
Every time the oscillator crosses over/under the outer bands the background will be highlighted.
Happy trading!
WaveTrend 3D█ OVERVIEW
WaveTrend 3D (WT3D) is a novel implementation of the famous WaveTrend (WT) indicator and has been completely redesigned from the ground up to address some of the inherent shortcomings associated with the traditional WT algorithm.
█ BACKGROUND
The WaveTrend (WT) indicator has become a widely popular tool for traders in recent years. WT was first ported to PineScript in 2014 by the user @LazyBear, and since then, it has ascended to become one of the Top 5 most popular scripts on TradingView.
The WT algorithm appears to have origins in a lesser-known proprietary algorithm called Trading Channel Index (TCI), created by AIQ Systems in 1986 as an integral part of their commercial software suite, TradingExpert Pro. The software’s reference manual states that “TCI identifies changes in price direction” and is “an adaptation of Donald R. Lambert’s Commodity Channel Index (CCI)”, which was introduced to the world six years earlier in 1980. Interestingly, a vestige of this early beginning can still be seen in the source code of LazyBear’s script, where the final EMA calculation is stored in an intermediate variable called “tci” in the code.
█ IMPLEMENTATION DETAILS
WaveTrend 3D is an alternative implementation of WaveTrend that directly addresses some of the known shortcomings of the indicator, including its unbounded extremes, susceptibility to whipsaw, and lack of insight into other timeframes.
In the canonical WT approach, an exponential moving average (EMA) for a given lookback window is used to assess the variability between price and two other EMAs relative to a second lookback window. Since the difference between the average price and its associated EMA is essentially unbounded, an arbitrary scaling factor of 0.015 is typically applied as a crude form of rescaling but still fails to capture 20-30% of values between the range of -100 to 100. Additionally, the trigger signal for the final EMA (i.e., TCI) crossover-based oscillator is a four-bar simple moving average (SMA), which further contributes to the net lag accumulated by the consecutive EMA calculations in the previous steps.
The core idea behind WT3D is to replace the EMA-based crossover system with modern Digital Signal Processing techniques. By assuming that price action adheres approximately to a Gaussian distribution, it is possible to sidestep the scaling nightmare associated with unbounded price differentials of the original WaveTrend method by focusing instead on the alteration of the underlying Probability Distribution Function (PDF) of the input series. Furthermore, using a signal processing filter such as a Butterworth Filter, we can eliminate the need for consecutive exponential moving averages along with the associated lag they bring.
Ideally, it is convenient to have the resulting probability distribution oscillate between the values of -1 and 1, with the zero line serving as a median. With this objective in mind, it is possible to borrow a common technique from the field of Machine Learning that uses a sigmoid-like activation function to transform our data set of interest. One such function is the hyperbolic tangent function (tanh), which is often used as an activation function in the hidden layers of neural networks due to its unique property of ensuring the values stay between -1 and 1. By taking the first-order derivative of our input series and normalizing it using the quadratic mean, the tanh function performs a high-quality redistribution of the input signal into the desired range of -1 to 1. Finally, using a dual-pole filter such as the Butterworth Filter popularized by John Ehlers, excessive market noise can be filtered out, leaving behind a crisp moving average with minimal lag.
Furthermore, WT3D expands upon the original functionality of WT by providing:
First-class support for multi-timeframe (MTF) analysis
Kernel-based regression for trend reversal confirmation
Various options for signal smoothing and transformation
A unique mode for visualizing an input series as a symmetrical, three-dimensional waveform useful for pattern identification and cycle-related analysis
█ SETTINGS
This is a summary of the settings used in the script listed in roughly the order in which they appear. By default, all default colors are from Google's TensorFlow framework and are considered to be colorblind safe.
Source: The input series. Usually, it is the close or average price, but it can be any series.
Use Mirror: Whether to display a mirror image of the source series; for visualizing the series as a 3D waveform similar to a soundwave.
Use EMA: Whether to use an exponential moving average of the input series.
EMA Length: The length of the exponential moving average.
Use COG: Whether to use the center of gravity of the input series.
COG Length: The length of the center of gravity.
Speed to Emphasize: The target speed to emphasize.
Width: The width of the emphasized line.
Display Kernel Moving Average: Whether to display the kernel moving average of the signal. Like PCA, an unsupervised Machine Learning technique whereby neighboring vectors are projected onto the Principal Component.
Display Kernel Signal: Whether to display the kernel estimator for the emphasized line. Like the Kernel MA, it can show underlying shifts in bias within a more significant trend by the colors reflected on the ribbon itself.
Show Oscillator Lines: Whether to show the oscillator lines.
Offset: The offset of the emphasized oscillator plots.
Fast Length: The length scale factor for the fast oscillator.
Fast Smoothing: The smoothing scale factor for the fast oscillator.
Normal Length: The length scale factor for the normal oscillator.
Normal Smoothing: The smoothing scale factor for the normal frequency.
Slow Length: The length scale factor for the slow oscillator.
Slow Smoothing: The smoothing scale factor for the slow frequency.
Divergence Threshold: The number of bars for the divergence to be considered significant.
Trigger Wave Percent Size: How big the current wave should be relative to the previous wave.
Background Area Transparency Factor: Transparency factor for the background area.
Foreground Area Transparency Factor: Transparency factor for the foreground area.
Background Line Transparency Factor: Transparency factor for the background line.
Foreground Line Transparency Factor: Transparency factor for the foreground line.
Custom Transparency: Transparency of the custom colors.
Total Gradient Steps: The maximum amount of steps supported for a gradient calculation is 256.
Fast Bullish Color: The color of the fast bullish line.
Normal Bullish Color: The color of the normal bullish line.
Slow Bullish Color: The color of the slow bullish line.
Fast Bearish Color: The color of the fast bearish line.
Normal Bearish Color: The color of the normal bearish line.
Slow Bearish Color: The color of the slow bearish line.
Bullish Divergence Signals: The color of the bullish divergence signals.
Bearish Divergence Signals: The color of the bearish divergence signals.
█ ACKNOWLEDGEMENTS
@LazyBear - For authoring the original WaveTrend port on TradingView
@PineCoders - For the beautiful color gradient framework used in this indicator
@veryfid - For the inspiration of using mirrored signals for cycle analysis and using multiple lookback windows as proxies for other timeframes
Nadaraya-Watson: Envelope (Non-Repainting)Due to popular request, this is an envelope implementation of my non-repainting Nadaraya-Watson indicator using the Rational Quadratic Kernel. For more information on this implementation, please refer to the original indicator located here:
What is an Envelope?
In technical analysis, an "envelope" typically refers to a pair of upper and lower bounds that surrounds price action to help characterize extreme overbought and oversold conditions. Envelopes are often derived from a simple moving average (SMA) and are placed at a predefined distance above and below the SMA from which they were generated. However, envelopes do not necessarily need to be derived from a moving average; they can be derived from any estimator, including a kernel estimator such as Nadaraya-Watson.
How to use this indicator?
Overall, this indicator offers a high degree of flexibility, and the location of the envelope's bands can be adjusted by (1) tweaking the parameters for the Rational Quadratic Kernel and (2) adjusting the lookback window for the custom ATR calculation. In a trending market, it is often helpful to use the Nadaraya-Watson estimate line as a floating SR and/or reversal zone. In a ranging market, it is often more convenient to use the two Upper Bands and two Lower Bands as reversal zones.
How are the Upper and Lower bounds calculated?
In this indicator, the Rational Quadratic (RQ) Kernel estimates the price value at each bar in a user-defined lookback window. From this estimation, the upper and lower bounds of the envelope are calculated based on a custom ATR calculated from the kernel estimations for the high, low, and close series, respectively. These calculations are then scaled against a user-defined multiplier, which can be used to further customize the Upper and Lower bounds for a given chart.
How to use Kernel Estimations like this for other indicators?
Kernel Functions are highly underrated, and when calibrated correctly, they have the potential to provide more value than any mundane moving average. For those interested in using non-repainting Kernel Estimations for technical analysis, I have written a Kernel Functions library that makes it easy to access various well-known kernel functions quickly. The Rational Quadratic Kernel is used in this implementation, but one can conveniently swap out other kernels from the library by modifying only a single line of code. For more details and usage examples, please refer to the Kernel Functions library located here:
Nadaraya-Watson non repainting [LPWN]// ENGLISH
The problem of the wonderfuls Nadaraya-Watson indicators is that they repainting, @jdehorty made an aproximation of the Nadaraya-Watson Estimator using raational Quadratic Kernel so i used this indicator as inspiration i just added the Upper and lower band using ATR with this we get an aproximation of Nadaraya-Watson Envelope without repainting
Settings:
Bandwidth. This is the number of bars that the indicator will use as a lookback window.
Relative Weighting Parameter. The alpha parameter for the Rational Quadratic Kernel function. This is a hyperparameter that controls the smoothness of the curve. A lower value of alpha will result in a smoother, more stretched-out curve, while a lower value will result in a more wiggly curve with a tighter fit to the data. As this parameter approaches 0, the longer time frames will exert more influence on the estimation, and as it approaches infinity, the curve will become identical to the one produced by the Gaussian Kernel.
Color Smoothing. Toggles the mechanism for coloring the estimation plot between rate of change and cross over modes.
ATR Period. Period to calculate the ATR (upper and lower bands)
Multiplier. Separation of the bands
// SPANISH
El problema de los maravillosos indicadores de Nadaraya-Watson es que repintan, @jdehorty hizo una aproximación delNadaraya-Watson Estimator usando un Kernel cuadrático racional, así que usé este indicador como inspiración y solo agregamos la banda superior e inferior usando ATR con esto obtenemos una aproximación de Nadaraya-Watson Envelope sin volver a pintar
Configuración:
Banda ancha. Este es el número de barras que el indicador utilizará como ventana retrospectiva.
Parámetro de ponderación relativa. El parámetro alfa para la función Rational Quadratic Kernel. Este es un hiperparámetro que controla la suavidad de la curva. Un valor más bajo de alfa dará como resultado una curva más suave y estirada, mientras que un valor más bajo dará como resultado una curva más ondulada con un ajuste más ajustado a los datos. A medida que este parámetro se acerque a 0, los marcos de tiempo más largos ejercerán más influencia en la estimación y, a medida que se acerque al infinito, la curva será idéntica a la que produce el Gaussian Kernel.
Suavizado de color. Alterna el mecanismo para colorear el gráfico de estimación entre la tasa de cambio y los modos cruzados.
Período ATR. Periodo para calcular el ATR (bandas superior e inferior)
Multiplicador. Separación de las bandas
KernelFunctionsLibrary "KernelFunctions"
This library provides non-repainting kernel functions for Nadaraya-Watson estimator implementations. This allows for easy substitution/comparison of different kernel functions for one another in indicators. Furthermore, kernels can easily be combined with other kernels to create newer, more customized kernels. Compared to Moving Averages (which are really just simple kernels themselves), these kernel functions are more adaptive and afford the user an unprecedented degree of customization and flexibility.
rationalQuadratic(_src, _lookback, _relativeWeight, _startAtBar)
Rational Quadratic Kernel - An infinite sum of Gaussian Kernels of different length scales.
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_relativeWeight : Relative weighting of time frames. Smaller values result in a more stretched-out curve, and larger values will result in a more wiggly curve. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Rational Quadratic Kernel.
gaussian(_src, _lookback, _startAtBar)
Gaussian Kernel - A weighted average of the source series. The weights are determined by the Radial Basis Function (RBF).
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Gaussian Kernel.
periodic(_src, _lookback, _period, _startAtBar)
Periodic Kernel - The periodic kernel (derived by David Mackay) allows one to model functions that repeat themselves exactly.
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period : The distance between repititions of the function.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Periodic Kernel.
locallyPeriodic(_src, _lookback, _period, _startAtBar)
Locally Periodic Kernel - The locally periodic kernel is a periodic function that slowly varies with time. It is the product of the Periodic Kernel and the Gaussian Kernel.
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period : The distance between repititions of the function.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Locally Periodic Kernel.
Nadaraya-Watson CombineThis is a combination of the Lux Algo Nadaraya-Watson Estimator and Envelope. Please note the repainting issue.
In addition, I've added a plot of the actual values of the current barstate of
the Nadaraya-Watson windows as they are computed (lines 92-95). It only plots values for the current data at
each time update. It is interesting to compare the trajectory of the end points of the Estimator and
Envelope to the smoothing function at each time update. Due to the kernel smoothing at each update the
history is lost at each update (repaint).
I've added a feature to allow adjustment to the kernel smoothing algorithm as suggested by thomsonraja (line 59).
The settings and usage are repeated from Lux Algo below.
Settings
Window Size: Determines the number of recent price observations to be used to fit the Nadaraya-Watson Estimator.
Bandwidth: Controls the degree of smoothness of the envelopes , with higher values returning smoother results.
Mult: Controls the envelope width.
Src: Input source of the indicator.
Kernel power: See line 59, adjusts the exponential power (powh) as suggested by thomsonraja
Kernel denominator: See line 59, adjusts the denominator (den) as suggested by thomsonraja
Usage
This tool outlines extremes made by the prices within the selected window size.
This is achieved by estimating the underlying trend in the price using kernel smoothing,
calculating the mean absolute deviations from it, and adding/subtracting it
from the estimated underlying trend.
I repeat Lux Algo's caution: 'we do not recommend this tool to be used alone
or solely for real time applications.'
Nadaraya-Watson: Rational Quadratic Kernel (Non-Repainting)What is Nadaraya–Watson Regression?
Nadaraya–Watson Regression is a type of Kernel Regression, which is a non-parametric method for estimating the curve of best fit for a dataset. Unlike Linear Regression or Polynomial Regression, Kernel Regression does not assume any underlying distribution of the data. For estimation, it uses a kernel function, which is a weighting function that assigns a weight to each data point based on how close it is to the current point. The computed weights are then used to calculate the weighted average of the data points.
How is this different from using a Moving Average?
A Simple Moving Average is actually a special type of Kernel Regression that uses a Uniform (Retangular) Kernel function. This means that all data points in the specified lookback window are weighted equally. In contrast, the Rational Quadratic Kernel function used in this indicator assigns a higher weight to data points that are closer to the current point. This means that the indicator will react more quickly to changes in the data.
Why use the Rational Quadratic Kernel over the Gaussian Kernel?
The Gaussian Kernel is one of the most commonly used Kernel functions and is used extensively in many Machine Learning algorithms due to its general applicability across a wide variety of datasets. The Rational Quadratic Kernel can be thought of as a Gaussian Kernel on steroids; it is equivalent to adding together many Gaussian Kernels of differing length scales. This allows the user even more freedom to tune the indicator to their specific needs.
The formula for the Rational Quadratic function is:
K(x, x') = (1 + ||x - x'||^2 / (2 * alpha * h^2))^(-alpha)
where x and x' data are points, alpha is a hyperparameter that controls the smoothness (i.e. overall "wiggle") of the curve, and h is the band length of the kernel.
Does this Indicator Repaint?
No, this indicator has been intentionally designed to NOT repaint. This means that once a bar has closed, the indicator will never change the values in its plot. This is useful for backtesting and for trading strategies that require a non-repainting indicator.
Settings:
Bandwidth. This is the number of bars that the indicator will use as a lookback window.
Relative Weighting Parameter. The alpha parameter for the Rational Quadratic Kernel function. This is a hyperparameter that controls the smoothness of the curve. A lower value of alpha will result in a smoother, more stretched-out curve, while a lower value will result in a more wiggly curve with a tighter fit to the data. As this parameter approaches 0, the longer time frames will exert more influence on the estimation, and as it approaches infinity, the curve will become identical to the one produced by the Gaussian Kernel.
Color Smoothing. Toggles the mechanism for coloring the estimation plot between rate of change and cross over modes.
STD-Filtered, Gaussian-Kernel-Weighted Moving Average [Loxx]STD-Filtered, Gaussian-Kernel-Weighted Moving Average is a moving average that weights price by using a Gaussian kernel function to calculate data points. This indicator also allows for filtering both source input price and output signal using a standard deviation filter.
Purpose
This purpose of this indicator is to take the concept of Kernel estimation and apply it in a way where instead of predicting past values, the weighted function predicts the current bar value at each bar to create a moving average that is suitable for trading. Normally this method is used to create an array of past estimators to model past data but this method is not useful for trading as the past values will repaint. This moving average does NOT repaint, however you much allow signals to close on the current bar before taking the signal. You can compare this to Nadaraya-Watson Estimator wherein they use Nadaraya-Watson estimator method with normalized kernel weighted function to model price.
What are Kernel Functions?
A kernel function is used as a weighing function to develop non-parametric regression model is discussed. In the beginning of the article, a brief discussion about properties of kernel functions and steps to build kernels around data points are presented.
Kernel Function
In non-parametric statistics, a kernel is a weighting function which satisfies the following properties.
A kernel function must be symmetrical. Mathematically this property can be expressed as K (-u) = K (+u). The symmetric property of kernel function enables its maximum value (max(K(u)) to lie in the middle of the curve.
The area under the curve of the function must be equal to one. Mathematically, this property is expressed as: integral −∞ + ∞ ∫ K(u)d(u) = 1
Value of kernel function can not be negative i.e. K(u) ≥ 0 for all −∞ < u < ∞.
Kernel Estimation
In this article, Gaussian kernel function is used to calculate kernels for the data points. The equation for Gaussian kernel is:
K(u) = (1 / sqrt(2pi)) * e^(-0.5 *(j / bw)^2)
Where xi is the observed data point. j is the value where kernel function is computed and bw is called the bandwidth. Bandwidth in kernel regression is called the smoothing parameter because it controls variance and bias in the output. The effect of bandwidth value on model prediction is discussed later in this article.
Included
Loxx's Expanded Source types
Signals
Alerts
Bar coloring
Nadaraya-Watson Envelope [LuxAlgo]This indicator builds upon the previously posted Nadaraya-Watson smoothers. Here we have created an envelope indicator based on Kernel Smoothing with integrated alerts from crosses between the price and envelope extremities. Unlike the Nadaraya-Watson estimator, this indicator follows a contrarian methodology.
Please note that by default this indicator can be subject to repainting. Users can use a non-repainting smoothing method available from the settings. The triangle labels are designed so that the indicator remains useful in real-time applications.
🔶 USAGE
🔹 Non Repainting
This tool can outline extremes made by the prices. This is achieved by estimating the underlying trend in the price, then calculating the mean absolute deviations from it, the obtained result is added/subtracted to the estimated underlying trend.
The non-repainting method estimates the underlying trend in price using an "endpoint Nadaraya-Watson estimator", and would return similar results to more classical band indicators.
🔹 Repainting
The repainting method makes use of the Nadaraya-Watson estimator to estimate the underlying trend in the price. The construction of the band extremities is the same as in the non-repainting method.
We can expect the price to reverse when crossing one of the envelope extremities. Crosses between the price and the envelopes extremities are indicated with triangles on the chart.
For real-time applications, triangles are always displayed when a cross occurs and remain displayed at the location it first appeared even if the cross is no longer visible after a recalculation of the envelope.
By popular demand, we have integrated alerts for this indicator from the crosses between the price and the envelope extremities. However, we do not recommend this precise method to be used alone or for solely real-time applications. We do not have data supporting the performance of this tool over more classical bands/envelope/channels indicators.
🔶 SETTINGS
Bandwidth: Controls the degree of smoothness of the envelopes, with higher values returning smoother results.
Mult: Controls the envelope width.
Source: Input source of the indicator.
Repainting Smoothing: Determine if a repainting or non-repainting method should be used for the calculation of the indicator.
🔶 RELATED SCRIPTS
For more information on the Nadaraya-Watson estimator see:
MathStatisticsKernelDensityEstimationLibrary "MathStatisticsKernelDensityEstimation"
(KDE) Method for Kernel Density Estimation
kde(observations, kernel, bandwidth, nsteps)
Parameters:
observations : float array, sample data.
kernel : string, the kernel to use, default='gaussian', options='uniform', 'triangle', 'epanechnikov', 'quartic', 'triweight', 'gaussian', 'cosine', 'logistic', 'sigmoid'.
bandwidth : float, bandwidth to use in kernel, default=0.5, range=(0, +inf), less will smooth the data.
nsteps : int, number of steps in range of distribution, default=20, this value is connected to how many line objects you can display per script.
Returns: tuple with signature: (float array, float array)
draw_horizontal(distribution_x, distribution_y, distribution_lines, graph_lines, graph_labels) Draw a horizontal distribution at current location on chart.
Parameters:
distribution_x : float array, distribution points x value.
distribution_y : float array, distribution points y value.
distribution_lines : line array, array to append the distribution curve lines.
graph_lines : line array, array to append the graph lines.
graph_labels : label array, array to append the graph labels.
Returns: void, updates arrays: distribution_lines, graph_lines, graph_labels.
draw_vertical(distribution_x, distribution_y, distribution_lines, graph_lines, graph_labels) Draw a vertical distribution at current location on chart.
Parameters:
distribution_x : float array, distribution points x value.
distribution_y : float array, distribution points y value.
distribution_lines : line array, array to append the distribution curve lines.
graph_lines : line array, array to append the graph lines.
graph_labels : label array, array to append the graph labels.
Returns: void, updates arrays: distribution_lines, graph_lines, graph_labels.
style_distribution(lines, horizontal, to_histogram, line_color, line_style, linewidth) Style the distribution lines.
Parameters:
lines : line array, distribution lines to style.
horizontal : bool, default=true, if the display is horizontal(true) or vertical(false).
to_histogram : bool, default=false, if graph style should be switched to histogram.
line_color : color, default=na, if defined will change the color of the lines.
line_style : string, defaul=na, if defined will change the line style, options=('na', line.style_solid, line.style_dotted, line.style_dashed, line.style_arrow_right, line.style_arrow_left, line.style_arrow_both)
linewidth : int, default=na, if defined will change the line width.
Returns: void.
style_graph(lines, lines, horizontal, line_color, line_style, linewidth) Style the graph lines and labels
Parameters:
lines : line array, graph lines to style.
lines : labels array, graph labels to style.
horizontal : bool, default=true, if the display is horizontal(true) or vertical(false).
line_color : color, default=na, if defined will change the color of the lines.
line_style : string, defaul=na, if defined will change the line style, options=('na', line.style_solid, line.style_dotted, line.style_dashed, line.style_arrow_right, line.style_arrow_left, line.style_arrow_both)
linewidth : int, default=na, if defined will change the line width.
Returns: void.
Nadaraya-Watson Smoothers [LuxAlgo]The following tool smoothes the price data using various methods derived from the Nadaraya-Watson estimator, a simple Kernel regression method. This method makes use of the Gaussian kernel as a weighting function.
Users have the option to use a non-repainting as well as a repainting method, see the USAGE section for more information.
🔶 USAGE
🔹 Non Repainting
When Repainting Smoothing is disabled the returned indicator acts similarly to a regular causal moving average. This result could be described as an "endpoint Nadaraya-Watson estimator".
Unlike a regular moving average whose degree of smoothness is commonly determined by the length of its calculation window, the degree of smoothness of the proposed indicator is determined by the bandwidth setting, with a higher value returning smoother results.
In the above chart, a bandwidth value of 50 is used. An increasing value of the smoother is indicative of an uptrend, while a decreasing value is indicative of a downtrend.
🔹 Repainting
Non-causal smoothing methods have found low support from technical analysts because they tend to repaint. Yet, they can provide powerful insights such as estimating underlying trends in the price as well as seeing how far prices deviate from them. They can also make drawing certain patterns easier and can help see underlying structures in the price more clearly.
Using higher bandwidth values allows for estimating longer-term trends in the price.
Triangular labels highlight points where the direction of the estimator change. This allows for the identification of tops and bottoms in the underlying trend which can be compared to the actual price tops and bottoms.
Note that multiple labels can appear in real time, highlighting real-time changes in the estimator's direction. The most recent label on a series of labels is the first to appear. This can eventually be useful for the real-time predictive application of the estimator. However, it is not a usage we particularly recommend.
🔶 DETAILS
The Nadaraya-Watson estimator can be described as a series of weighted averages using a specific normalized kernel as a weighting function. For each point of the estimator at time t , the peak of the kernel is located at time t , as such the highest weights are attributed to values neighboring the price located at time t .
A lower bandwidth value would contribute toward a more important weighting of the price at a precise point and would as such less smooth results. In the case where our bandwidth is so small that the resulting kernel is just an impulse, we would get the raw price back.
However, when the bandwidth is sufficiently large, prices would be weighted similarly, thus resulting in a result closer to the price mean.
It can be interesting to note that due to the nature of the estimator and its weighting procedure, real-time results would not deviate drastically for points in the estimator near the center of the calculation window.
🔶 SETTINGS
Bandwidth : controls the bandwidth of the Gaussian kernel, with higher values returning smoother results.
Src : Input source of the kernel regression.
Repainting Smoothing : Determine if the smoothing method should repaint or not. If disabled the "endpoint Nadaraya-Watson estimator" is returned.
