Based on the exponential averaging method with lag reduction, this filter allow for smoother results thanks to a multi-poles approach. Translated and modified from the Non-Linear Kalman Filter from Mladen Rakic 01/07/19 mql5.com/en/code/24031
The Indicator
length control the amount of smoothing, the poles can be from 1 to 3, higher values create smoother results.
Difference With Classic Exponential Smoothing
A classic 1 depth recursion (Single smoothing) exponential moving average is defined as y = αx + (1 - α)y which can be derived into y = y[1] + α(x - y[1])
2 depth recursion (Double smoothing) exponential moving average sum y with b in order to reduce the error with x, this method is calculated as follow :
y = αx + (1 - α)(y[1] + b)
b = β(y - y[1]) + (1-β)b[1]
The initial value for y is x while its 0 for b with α generally equal to 2/(length + 1)
The filter use a different approach, from the estimation of α/β/γ to the filter construction.The formula is similar to the one used in the double exponential smoothing method with a difference in y and b
y = αx + (1 - α)y[1]
d = x - y
b = (1-β)b[1] + d
output = y + b
instead of updating y with b the two components are directly added in a separated variable. Poles help the transition band of the frequency response to get closer to the cutoff point, the cutoff of an exponential moving average is defined as :
Cf = F/2π acos(1 - α*α/(2(1 - α)))
Also in order to minimize the overshoot of the filter a correction has been added to the output now being output = y + 1/poles * b
While this information is far being helpful to you it simply say that poles help you filter a great amount of noise thus removing irregularities of the filter.
Conclusion
The filter is interesting and while being similar to multi-depth recursion smoothing allow for more varied results thanks to its 3 poles.
Thank you @alexgrover for creating and publishing this Awesome Script !!! :)
I have put 7 of them on my chart @ lengths :5,15,30,60,90, 180 , and 360 (hlc3)
I have no idea how it works but I have used it every day for over 6 months now
and I have to say I really like the indicator
this is an underrated gem in my view
Thank you for being an inspiration to new pinescript enthusiasts
in my view your "Multi Depth Zero-Lag Exponential Moving Average" is the best thing since the classic "EMA" ribbon
I would also have to shout out the McGinley Dynamic as it is a favourite of my as well
and I all most for got the Vwap
after a bit of poking and prodding I was able to modify the script to be V4 compatible
when I get a bit better than I am now
I hope to have a ribbon of many lengths of this indicator in one script :)
Thank you kindly
alexgrover
⋅
@iamthree, Thanks a lot for your comment :) I am glad to hear your are using the indicator and that I could inspire others with my code, it means a lot ^^
I have put 7 of them on my chart @ lengths :5,15,30,60,90, 180 , and 360 (hlc3)
I have no idea how it works but I have used it every day for over 6 months now
and I have to say I really like the indicator
this is an underrated gem in my view
Thank you for being an inspiration to new pinescript enthusiasts
in my view your "Multi Depth Zero-Lag Exponential Moving Average" is the best thing since the classic "EMA" ribbon
I would also have to shout out the McGinley Dynamic as it is a favourite of my as well
and I all most for got the Vwap
after a bit of poking and prodding I was able to modify the script to be V4 compatible
when I get a bit better than I am now
I hope to have a ribbon of many lengths of this indicator in one script :)
Thank you kindly