The ability to reduce lag while keeping a good level of stability has been a major challenge for smoothing filters in . Stability involve many parameters, one of them being overshoots. Overshoots are a common effect induced by low-lagging filters, they are defined as the ability of a signal output to exceed a target input. This effect can lead to major drawbacks such as whipsaw and reduction of precision. I propose a modification of the "Reduced Overshoots Moving Average" (ROMA) to reduce overshoots induced by the by using a scaled recursive dispersion coefficient with the purpose of reducing overshoots.
Overshoots - Causes and Effects
Control theory and electronic engineering use step response to measure overshoots, the target signal is defined as an heaviside step function which will be used as input signal for our filter.
In white an input signal, in blue a with the input signal as source, the circle show the overshoot induced by the , the filter exceed drastically the target input. But why low lag filters often induce overshoots ? This is because in order to reduce lag those filter will increase certain frequencies of the input signal, this reduce lag but induce overshoots because the amplitude of those frequencies have been increased, so its normal for the filter to exceed the input target. The increase of frequencies is not a bad process but when those frequencies are already of large amplitudes (high periods) the overshoots can be seen.
Comparison With ROMA
Our method will use the line rescaling technique to estimate the for efficiency sake. This method involve calculating the z-score of a line and multiplying it by the correlation of the line and the target input (price). Then we rescale this result by adding this z-score multiplied by the dispersion coefficient to a . Lets compare the step response of our filer and the .
ROMA (in red) need more data to be computed but reduce the mean absolute error in comparison with the classic , it is seen that instead of following increasing, ROMA decrease thus ending with an undershoot.
ROMA in (red) and an (in blue) with both length = 14, ROMA decrease overshoots with the cost of less smoothing, both filter match when there are no overshoots situations.
Both filters with length = 200, large periods increase the amplitude of overshoots, ROMA stabilize early at the cost of some smoothness.
The running Mean Absolute Error of both filters with length = 100, ROMA (in red) is on average closer to the price than the (in blue)
I presented a modification of the with the goal to provide both stability and rapidity, the statistics show that ROMA do a better job when it comes to reduce the mean absolute error. Alternatives methods can involve decreasing the period it take for the filter to be on a steady state (reducing filter period during high periods), various filters already exploit this method.
I'am not that good when it come to make my post easy to read, this is why i'am currently making an article explaining the basis of digital signal processing. This post will help you to understand signals and things such as lag, frequency transform, cycles, overshoots, ringing, FIR/IIR filters, impulse response, convolution, filter topology and many more. I love to post indicators but also making more educational content as well, so stay tuned :)
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