SteveNYC: A chart of a lowpass filter was posted here some months ago, look for a thread titled like "extremely simple profitable strategies" or similar. And no, I do not day trade. My computer does.
You mean second or higher order filters work, I guess. First order low pass = exponential moving average. So you are saying that going from first order to second order filters makes an unprofitable system become profitable. I suppose it's plausible, but I still haven't had the chance to check.
If a system is profitable depends on many factors, not alone on the filter. But it's certainly easier to write a profitable system with a second order filter, than with an EMA. The filter catches market changes earlier because it has far less lag. You can easily test this when you have a trade platform with a C style language - just replace the EMA with my code above.
This filter certainly has the characteristic frequency response of a low pass filter. Unfortunately the charting tools I use don't have the capability to evaluate it but I note it can be rewritten as: EMA( EMA( (1/a-0.25)*Data[0]+0.24*Data[1]-(1/a-0.75)*Data[2] )) where EMA is the standard EMA function. Why not use the zero lag EMA which is first order and not as lagging as a standard EMA, although it isn't a low pass filter: EMA( 2*Data[0]-Data[k] ) with k=1 or k=2
I haven't heard yet from the zero lag EMA indicator, but if I understand your formula correctly, it's the EMA of the price momentum. This is more a highpass filter than a low pass filter, and has certainly not zero lag.