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Moving Regression
Updated
Moving Regression is a generalization of moving average and polynomial regression.
The procedure approximates a specified number of prior data points with a polynomial function of a user-defined degree. Then, polynomial interpolation of the last data point is used to construct a Moving Regression time series.
Application:
Moving Regression allows one to smooth noise on the analyzed chart, assess momentum, confirm trends, and establish areas of support and resistance.
In addition, it can be used as a simple stand-alone forecasting method to identify trend direction and trend reversal points. When the local polynomial is predicted to move up in the next time step, the color of the Moving Regression curve will be green. Otherwise, the color of the curve is red. This function is (de)activated using the Predict Trend Direction flag.
Selecting the model parameters:
The effects of the moving window Length and the Local Polynomial Degree are confounded. This allows for finding the optimal trade-off between noise (variance) and lag (bias). Higher Length and lower Polynomial Degree (such as 1, i.e. linear), will result in "smoother" time series but at the cost of greater lag. Increasing the Polynomial Degree to, for example, 2 (squared) while maintaining the Length will diminish the lag and thus compromise the noise-lag tradeoff.
Relation to other methods:
When the degree of the local polynomial is set to 0 (i.e., fitting data to a constant level), the Moving Regression time series exactly matches the Simple Moving Average of the same length.
The procedure approximates a specified number of prior data points with a polynomial function of a user-defined degree. Then, polynomial interpolation of the last data point is used to construct a Moving Regression time series.
Application:
Moving Regression allows one to smooth noise on the analyzed chart, assess momentum, confirm trends, and establish areas of support and resistance.
In addition, it can be used as a simple stand-alone forecasting method to identify trend direction and trend reversal points. When the local polynomial is predicted to move up in the next time step, the color of the Moving Regression curve will be green. Otherwise, the color of the curve is red. This function is (de)activated using the Predict Trend Direction flag.
Selecting the model parameters:
The effects of the moving window Length and the Local Polynomial Degree are confounded. This allows for finding the optimal trade-off between noise (variance) and lag (bias). Higher Length and lower Polynomial Degree (such as 1, i.e. linear), will result in "smoother" time series but at the cost of greater lag. Increasing the Polynomial Degree to, for example, 2 (squared) while maintaining the Length will diminish the lag and thus compromise the noise-lag tradeoff.
Relation to other methods:
When the degree of the local polynomial is set to 0 (i.e., fitting data to a constant level), the Moving Regression time series exactly matches the Simple Moving Average of the same length.
Release Notes
minor correctionsOpen-source script
In true TradingView spirit, the author of this script has published it open-source, so traders can understand and verify it. Cheers to the author! You may use it for free, but reuse of this code in publication is governed by House rules. You can favorite it to use it on a chart.
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