f(alpha) > 1?
settwi opened this issue · 11 comments
Hi there,
I was under the impression that when investigating multifractal spectra, f(alpha) should not rise above 1. Running the example notebook it looks like that f(alpha) > 1 for some (negative?) moments q.
I'm no expert on multifractal spectra, but I've been trying to apply the formalism using WTMM to some solar flare X-ray data for a while, using a Python adaptation from this paper 2007ApJ...662..691M. Usually when spectra make odd shapes like that, they are either noisy, or the algorithm is busted.
Thoughts and/or references?
I can put my code up on a public GitHub too if that would be helpful.
Best
William
Pretty sure I had an issue with window widths.
If the windows don't cover a wide enough range the multifractal spectrum gets polluted.
Overall, this package is fast and works better than an implementation of WTMM I've been working on. Thank you!!!!!!
Hi William, sorry for the very late reply, these months I was very busy.
Glad to know the issue is resolved.
Just to know, did you also have a change in the concavity of the spectrum when f(alpha) > 1?
Yeah, it was concave up.
hey just a followup question about the MFDFA routines.
do you have a version that implement the Y(i) as in eq. 7 in Kantelhardt+2002?
they note:
However, the MF-DFA method can only determine positive generalized Hurst exponents h(q), and it already becomes inaccurate for strongly anti-correlated signals when h(q) is close to zero. In such cases, a modifed (MF-)DFA technique has to be used.
Might be a nice addition to add, and not too much more work. similar fluctuation function definition...
- WS
Also would be nice to implement the logarithmic summation for q = 0.
Maybe I can open a pull request at some point with some additions :)
Hi William,
I'll look into it.
The logarithmic summation for q = 0 is already implemented. Did you notice inconsistencies for q = 0?
I was getting nans when q = 0 and a divergent situation with q -> 0. i’ll double check today though. if i find a particular data set that causes issues i’ll send it your way!
Looks like I probably had an error somewhere else. q = 0 gives sensible results as far as I can tell.
ok thanks. I'm also noticing a divergence for q->0, I'm making some tests and will release a fix asap
Thank you!