Quote from stephencrowley:
Where did you get this idea?
"Gaussian Self-Affinity and Fractals: Globality, the Earth, 1/F Noise, and R/S"
Fractal/chaotic processes are clearly predictible in the short term if you have enough data, find the proper embedding and then find the appropriate lower-dimensional phase space representation.
See 'Taken's theorem'.
Price series can be realized as the output of a high-dimensional but semi-deterministic process, reconstructing this process is an ill-posed inverse problem where you have to reverse engineer the actual/hidden process generating this data.
stephencrowley,
You are contradicting Mandelbrot. Mandelbrot has always modelled price fluctuations as a fractal but
unpredictable process. He hasn't excluded the possiblity that price changes can be predicted, but none of his models or theories even attempt to provide any directional price predictions, or to suggest that such would even be possible. If my information is out of date, then please post an exact page number and an exact quotation supporting your position.
Mandelbrot has never, ever claimed that all fractal processes can be predicted using the method you describe. I challenge you to give an exact page number and an exact quotation where he says such a thing. I would go even further, to say that no reputable, respected scientist has ever made such a claim. My guess is that you don't really understand what the word "fractal" really means.
You claim that the embedding theorem, due to Takens, applies to price series, but Mandelbrot never made such a claim, and neither did Takens. The embedding theorem only applies to certain types of systems. Nobody has ever demonstrated that price fluctuations fit the requirements and assumptions necessary before the Takens embedding theorem can be applied.
Nobody has ever demonstrated your other claim, that price changes exhibit low-dimensional chaos. The foremost experts and founders of chaos theory made extensive efforts to demonstrate this, but then gave up on the effort. These include people like Farmer, Packard, and others at the Prediction Company. Mandlebrot has also never claimed that price changes show low-dimensional chaos. If my information is out of date, then please post an exact page number with an exact quotation.
It is possible that prices do involve low-dimensional chaos, but this has never been demonstrated. If, as I and many others believe, prices are somewhat predictable, this does not imply that they also have low-dimensional chaos. It is not necessary to have low-dimensional chaos in order for prices, or any other series, to have some predictability.
My suspicion is that you have no real understanding of the scientific literature you are discussing, and that you are throwing around jargon without knowing how the terms are actually defined. This leads me to doubt the validity of your claims that you are using such literature as the basis for price predictions.
