Dear Prof. Marri,

                            In doing any time series analysis whether using structured data or live data you have to compute the correlations vectorially in order for a machine language to compute from basics, hence factorisation and scaling, which are possible with fractal geometric resolution of the graphs can be used. I don't know whether that gives the only technology. I hope it helps. SKM QC

The best comparative analysis of different algorithms You can find in a paper:

Ihlen, E.A.F., 2013. Multifractal analyses of response time series: A comparative study. Behav Res 45, 928–945. doi:10.3758/s13428-013-0317-2

I found an article by LA Smith, ``The Maintenance of Uncertainty'', to be very enlightening on this whole topic, though it may, in fact, cover a bit more than you ask for:

http://www2.maths.ox.ac.uk/~lenny/fermi96_main_abs.html

Kiran, the main issue is that once you obtain the dimension exponent or the spectrum of dimensions, you still need to find the interpretation for your result. This is the essential 'so what' question which you need to answer. There are a range of technical 'issues' or 'drawbacks' but they pale in comparison with the above. Among the major technical problems, the extent of the scaling range is crucial. It is often too short to be meaningful (less than two decades of scaling). This applies both to fractal dimension and spectra estimation. In this context it is essential to provide error bars and determine significance of the results. Methods for doing this (via bootstrapping, etc) have been published for the wavelet based approaches but to a lesser extent on DFA etc, where it is actually almost straightforward (although not always performed). One difficulty in doing the analysis both using the DFA and wavelets is the choice of the degree of detrending and the number of vanishing moments of the wavelet - per default, there is full freedom there but one should determine if/how this choice affects the results. Ideally, the choice would not influence the results (at least for degrees/moments greater than some minimum value).

Herewith some drawbacks of fractal dimension, so an alternative index ht-index was developed:

Jiang B. and Yin J. (2014), Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104(3), 530–541.

https://www.researchgate.net/publication/236627484_Ht-Index_for_Quantifying_the_Fractal_or_Scaling_Structure_of_Geographic_Features?ev=prf_pub

Article Ht-Index for Quantifying the Fractal or Scaling Structure of...