Short Term Trading Member Forum

[techcharter]

MrCash: Cycle Variance

I'm very well aware of cycle variances. It's one of the reasons a highly selective bandpass filter has inaccuracies. Infitnite impulse response filters have inertial problem to deal with. It can take 4 to 5 cycles of a pure sine wave before the transient response has settled. Hurst uses a moving average which is a finite impulse response filter. The problem with that is it lags in time by half the number days in the average.

I tried using Fourier Series last night. It takes little time when using a spreadsheet. The problem with Fourier Series signal analysis is the largest period is equal to the number of samples. If you didn't know there was a 4.5 year cycle, you could mis it. Another problem is the next largest cycle is half the number of days of samples. Hurst shows how the cycles are generally separated between 33% and 50%, Fourier would miss those cycles. Gibbs phenomena introduces overshoot at the ends of the sample range. Truncating the series above some frequency would reduce the ringing, but there is still a more fundamental problem. Fourier series is it is based on the pattern of the samples repeating. The market does not repeat that way. If it did, we would not need analysis. This invalidates the curve approximatino at the very end of the sample range where highly accurate prediction is most desired.