Re: FFT of stock market data?



A couple of things:

1) people do use FFT (or other spectral analysis techniques) to price
series.

2) yes, price series can be non-stationary. for most of the price
series, take log (natural logarithm) of the price series. it remove
seasonality to much extent. more over, a moving average can also be
used to detrend. standard detrend function is not useful here.

3) the problem with FFT is resolution of time periods, what you get.
Moreover, ignore first time-period value (=0), also the first number
after fft is a real number, just the sum of data. thus T(1) = [].
search for Sunspot example on mathworks site, for the simplest
analysis to detect cyclicity.

4) params for FFT: issues like whether to use any filters, whether to
use zeo-padding or data truncation etc etc comes up. For most of the
price series, spectral analysis, with simple fft (without
zero-padding and Filters) works.

5) There is no way to confirm whether the detected (local) peaks of
the spectrum gives to corresponding time periods. They just give you
a hint. Interaction, echos and overtones might be creating peaks on
the spectrum, yet actual data may not contain that period or cycle.
Thus, another Test of significance method is needed.

6) Test of significance: there are tests like F-test, chi-test and
Bartels test to check the significance of a particular cycle/ period
under investigation. Bartels test of the most significant one.

7) alternate ways : wavelett theories, MESA (maximum entropy spectral
analysis) are two other significant schools of ideas for Cycle
research. you might like those ideas too.

There is much more to cycle research before one can think of applying
it for practical trading. People have been working for years (40-50
years) in this area. if i remember correctly, cycle research
foundation and a couple of similar sites provides you more info.
.