I have several of Tomes' URLS I will post later.
Fourier has to use a 256 point or root of 2 number of points usually. This limits it usually from being used as an ongoing analysis too. But there is software out that does fourier without needing the root of two number of points. (It's commercial, URL later)
Theoretically if the software is flexible enough, it should allow the "one more point" to be added and analysed, allowing an ongoing predictor.
One way you apply fourier and regression is to first get your spectrum and visually or with a filter pick out your cycles that you wish to extend. This is artistic so to speak because fourier creates many small cycles that are really noise. The higher amplitude ones and the more dominant ones are picked and tried. Usually you can stop at say seven important ones. Each cycle is extended by some means and the resultant wave is recombined. Add more cycles until the wave is better reproduced for the longest period.
Regression, either linear or non linear can work with each cycle. The means of recombination does not actually have to be reverse fourier it may be any sort of sine wave recombination allowing a zero crossing detection. We assume a sero crossing midway between peaks of the phase spectra graph.
I am not sure that fourier gives the best phase info. If you experiment with different starting points or phases of observed smaller cycles produced by fourier you may actually clean your data a bit of the resultant recombined wave. A sort of trial fourier can be done which "assumes" dominant cycles for a stock or index, and combines them with different phase offsets in a trial fit. This is basically what Kondratieff did by recombining all the various micro cycles of prices to produce a more regressable (from the previous micro cycles) macro cycle of the economy.
A good charting tool would be one that allowed you to experiment with different waves. you could select an amplitude, frequency and perhaps shape too, either suggested by analysis, of any kind, or by inspection or guess, and superimpose it and shift its phase by cut and past and click. The power of being able to select a say, saw tooth wave of 4 hours or 4 days and 3.5% and testing different starting points for a fit is not present in most software out there. Just foolin around intuitively might build the best wave fit. Pooters can show you what you might not guess about cycles, but they don't know the what of lunch hours, or weekends or monday hangovers.
The largest cycles are not too difficult to see. The computer once fed the phase and amplitude of of the large fluxes, can then pile on trial smaller fluxes with different frequencies and phases until the curve starts to fit the observed one. Shifting phases is "cheating" a bit, and more computation but fourier cannot not know "real" phases or the real flux underneath, it cheats by coming up with different frequencies of sines or cosines to compensate.
The purist does not care about the fundamentals. In a way all the info is there in the price and volume. Fundamentals and technical analysis are not that far apart and one that ignores the other is a bit strange. How can the Technical stock analysis "see" a sudden plan by management to do a merger? One way of looking at this is to assume that there are no sudden decisions and that there will be some trading into this decision that will "presage or change the cycle beforehand" In fact bottom feeder systems utilizing trading range and on balance volume indicators, that are wildly successful, like canadianmarketwatch.com do just that. Admittedly they could use fundamental refinement as they themselves say.
It would be foolish to ignore known "causes". News announcments, insider dope etc.. Other traders react to them anyway, so it is a good idea to go with the flow.
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