A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation

[LRydin]

A recent paper in Physica A, entitled A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation (Physica A 565, p125611, 2021) suggests a set of "complicated" functions to serve as fitting for each segmentation, replacing the simple polynomial fittings. These include a combination of polynomial and trignometric functions, which are meant to minimise the mean absolute error for each fit of a segment.

We can consider implementing this, likely at the cost of performance as we likely require scipy's fit, which I believe in single-threaded. The approach seems simple enough to constitute an interesting addition to MFDFA.

[00stat]

I have already read this paper. How can I improve the use of this method in the source code

[LRydin]

Hey @00stat, sorry for the delay, I was away last week. Well, if you'd like to help, we need create a new function similar to MFDFA and fundamentally "wrap" L210-211 with a curve_fit function from scipy. curve_fit can then take all the detrendings suggested in the paper.

The primary issue here is that a large amount of these functions will perfectly fit the data, so we have to test what is the minimum lag that can be accepted for each, which will likely have to be a bit of guesswork.

What do you think?

[00stat]

I'm sorry for taking so long to see your message. I think your ideas have given me great inspiration. I will consider modifying the source code you provided in the next few days