Two traditional methods to generate long range correlations are Fourier Filtering Method (FFM) and Makse algorithm. But, due to the limitations of the Fourier transform these two methods are not flexible enough to simulate issues like mid-way frequency change in the signal. Is there any way to use Wavelet to simulate a signal with long range dependence?
Why wavelets? If you want to quickly simulate a signal with long-range structure, just filter a white-noise input with an IIR filter with transfer function H(z) = B(z)/A(z). The frequency response H(w) is found by substituting z = exp(i*w) in H(z). The filter coefficients b(m) & a(m) of your IIR filter are taken from the polynomials B(z) and A(z) respectively.
Dear Hugh, thanks for your answer.
That's a pretty good idea.
It seems that it only gives anti-correlated series (in practice) unless the filter is applied to a noise of higher DFA (or even the Hurst exponent). Or there is any other measure to quantify noise....
Though, I haven't yet managed to get the logic for how IIR filtering can simulate long-range dependence.
Many thanks
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