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.
Nonlinearregression
GKYZ-Filtered, Non-Linear Regression MA [Loxx]GKYZ-Filtered, Non-Linear Regression MA is a Non-Linear Regression of price moving average. Use this as you would any other moving average. This also includes a Garman-Klass-Yang-Zhang Historical Volatility Filter to reduce noise.
What is Non-Linear Regression?
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.
What is Garman-Klass-Yang-Zhang Historical Volatility?
Yang and Zhang derived an extension to the Garman Klass historical volatility estimator that allows for opening jumps. It assumes Brownian motion with zero drift. This is currently the preferred version of open-high-low-close volatility estimator for zero drift and has an efficiency of 8 times the classic close-to-close estimator. Note that when the drift is nonzero, but instead relative large to the volatility , this estimator will tend to overestimate the volatility . The Garman-Klass-Yang-Zhang Historical Volatility calculation is as follows:
GKYZHV = sqrt((Z/n) * sum((log(open(k)/close( k-1 )))^2 + (0.5*(log(high(k)/low(k)))^2) - (2*log(2) - 1)*(log(close(k)/open(2:end)))^2))
Included
Alerts
Signals
Loxx's Expanded Source Types
Bar coloring
