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4. Concluding remarks

As a general rule, Legendre spectra will yield more robust results, but will wipe out any departure from concavity in the spectrum. It is often a good idea to compute both fg and fl. If fl is approximately the concave hull of fg, then it is reasonable to assume that the estimates of both fg and fl are relevant. Also, you'll find that, in most cases, pure time-domains estimates of the spectra give better results. An interesting test in that view is to synthesize a multifractal measure, using the measure sub-menu of the synthesis menu with the default parameters (this will yield a trinomial measure at resolution 7). Try then the estimation of both fg and fl using all methods above, i.e. DWT-based, CWT-based and box method for fl, and the kernel method for fg. In all cases, use the default or basic parameters. You'll see how the box-method estimate of fl agrees reasonably well with the kernel estimate of fg, as it should. Also, the theoretical spectrum (which Fraclab may compute at the same time it synthesizes the measure) agrees quite well with these estimates of fl and fg. Both wavelet estimators are quite off.


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