Ive simulated data with specific alpha. Why do I get different slopes using DFA or FFT analysis ?
First of all, the slopes that measured by DFA and FFT methods are not equivalent and the relation between them is the following alpha=beta+1/2 where alpha is slope got from DFA and beta from FFT . Moreover, there are some restrictions on the range of the slopes in which DFA and FFT should produce a correct results. For example, DFA algorithm never can give alpha which is smaller than 0 or greater than n+1 where n is the order of DFA. It was also found that we can “trust” DFA algorithm only if alpha we got is greater than 1/2 and smaller than n+1/2 . We should also remember that simulated data is also produced by other algorithm (Wavelet) that has its own restrictions (e.g. data is too short). Of course all these restrictions are not taken for granted but based on some mathematical explanation.
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