I just don't see frequency transforms doing much good on what is essentially noise. Are the markets cyclical? Maybe, but the periods and amplitudes constantly shift do to whatever economic, demographic, political, terrorist...whatever, forces are pushing/pulling the most. IOW you are still taking totally random waveforms and trying to make sense of them. You are just curve-fitting and fooling yourself. Sentiment, as expressed in OB/OS and fear/greed with a smattering of momentum, tape reading and order imbalance tricks like Don's openings and early identification of "fundies" if possible is the way to go to make money IMHO, at least in equities. Certainly, hitting the markets with that level of maths and transforms ain't worth the trouble.
I used f, 2*f, 4*f as an example. Phases should be there, else I should use cosine factors. For 3 summands used in my example I would need 3 cosine terms, ie 3 more amplitudes and the iteration would be longer. As you see from the code, phi goes from 0 to 2*pi, step pi/12 and introduces [only] 12 steps.
When we use linearreg, it doesn´t mean the markets are linear. Linearreg gives a first, crude approximation of an oscillator with two main info :Ascending [or not] and how much. The linearreg line is not steady, tomorrow it will have another slope, but it is not a problem. The above exposed sinusoidal analysis is much more informative than the linearreg approach.
I use as example the function f=10+3.8*sin(2*pi*(1/384)*(t-t1)+13*pi/12)+1.2*sin(2*pi*(1/216)*(t-t1)+3*pi/12) ie a superposition of two sinusoidals with periods 384 and 216.[red line] The above chart is the Fourier analysis with per, per/2, per/4.[white line] Below is per, per/3, per/5 [white line] Phases go from 0 to 2*pi, srep pi/12 in both investigations. The error/bar is similar and, the most important, below 2%
And Harrytrader' mission in life is to tell people how crap ANY "sophistical" tools are IF you don't know how real market works. If you know at least enough bit to be operational - since a model by definition never encompass total reality - it can be different and fruitfull to use some tools FFT, Wavelet, NN or others . But since most ignore how real market works they play with these tools like Monkeys hoping that by magic the tools would create a working model for them. See http://www.elitetrader.com/vb/showthread.php?s=&threadid=28614&highlight=Neural+and+networks ANNs: A Little Knowledge Can Be A Dangerous Thing Posted by Dr. Halbert White
Hello, I don't think you can necessarily discredit the use of FFT's in all aspects of trading analysis. I would probably agree that it isn't efficient to apply Fourier transforms to price data, but applying a fast fourier transform to price volatility is another thing... Joe