STD-Filtered, N-Pole Gaussian Filter [Loxx]

Updated

This is a Gaussian Filter with Standard Deviation Filtering that works for orders (poles) higher than the usual 4 poles that was originally available in Ehlers Gaussian Filter formulas. Because of that, it is a sort of generalized Gaussian filter that can calculate arbitrary (order) pole Gaussian Filter and which makes it a sort of a unique indicator. For this implementation, the practical mathematical maximum is 15 poles after which the precision of calculation is useless--the coefficients for levels above 15 poles are so high that the precision loss actually means very little. Despite this maximal precision utility, I've left the upper bound of poles open-ended so you can try poles of order 15 and above yourself. The default is set to 5 poles which is 1 pole greater than the normal maximum of 4 poles.

The purpose of the standard deviation filter is to filter out noise by and by default it will filter 1 standard deviation. Adjust this number and the filter selections (price, both, GMA, none) to reduce the signal noise.

What is Ehlers Gaussian filter?
This filter can be used for smoothing. It rejects high frequencies (fast movements) better than an EMA and has lower lag. published by John F. Ehlers in "Rocket Science For Traders".

A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve. In the case of low-pass filters, only the upper half of the curve describes the filter. The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of high-frequency components relative to the lag of lower-frequency components.

A gaussian filter with...

One Pole: f = alpha*g + (1-alpha)f[1]
Two Poles: f = alpha*2g + 2(1-alpha)f[1] - (1-alpha)2f[2]
Three Poles: f = alpha*3g + 3(1-alpha)f[1] - 3(1-alpha)2f[2] + (1-alpha)3f[3]
Four Poles: f = alpha*4g + 4(1-alpha)f[1] - 6(1-alpha)2f[2] + 4(1-alpha)3f[3] - (1-alpha)4f[4]
and so on...

For an equivalent number of poles the lag of a Gaussian is about half the lag of a Butterworth filters: Lag = N*P / pi^2, where,
N is the number of poles, and
P is the critical period

Special initialization of filter stages ensures proper working in scans with as few bars as possible.

From Ehlers Book: "The first objective of using smoothers is to eliminate or reduce the undesired high-frequency components in the eprice data. Therefore these smoothers are called low-pass filters, and they all work by some form of averaging. Butterworth low-pass filters can do this job, but nothing comes for free. A higher degree of filtering is necessarily accompanied by a larger amount of lag. We have come to see that is a fact of life."

References John F. Ehlers: "Rocket Science For Traders, Digital Signal Processing Applications", Chapter 15: "Infinite Impulse Response Filters"

Included

Loxx's Expanded Source Types
Signals
Alerts
Bar coloring

Related indicators

STD-Filtered, Gaussian Moving Average (GMA) [Loxx]

STD-Filtered, Gaussian-Kernel-Weighted Moving Average

One-Sided Gaussian Filter w/ Channels

Fisher Transform w/ Dynamic Zones

R-sqrd Adapt. Fisher Transform w/ D. Zones & Divs .

Release Notes

Updated code to be more efficient by creating coefficients only one time. Also updated source type callers to be more efficient. Thanks to lejmer for the suggestions!

Open-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.

Want to use this script on a chart?

loxx

Public Telegram Group, t.me/algxtrading_public

VIP Membership Info: patreon.com/algxtrading/membership

Also on:

Disclaimer

The information and publications are not meant to be, and do not constitute, financial, investment, trading, or other types of advice or recommendations supplied or endorsed by TradingView. Read more in the Terms of Use.