Investigation on series of length of coding and non-coding DNA sequences of bacteria using multifractal detrended cross-correlation analysis.

In the framework of multifractal detrended cross-correlation analysis, we investigate characteristics of series of length of coding and non-coding DNA sequences of some bacteria and archaea. We propose the use of a multifractal cross-correlation series that can be defined for any pair of equal lengths data sequences (or time series) and that can be characterized by the full set of parameters that are attributed to any time series. Comparison between characteristics of series of length of coding and non-coding DNA sequences and of their associated multifractal cross-correlation series for selected groups is used for the identification of class affiliation of certain bacteria and archaea. The analysis is carried out using the dependence of the generalized Hurst exponent on the size of fluctuations, the shape of the singularity spectra, the shape and relative disposition of the curves of the singular measures scaling exponent and the values of the associated parameters. Empirically, we demonstrate that the series of lengths of coding and non-coding sequences as well as the associated multifractal cross-correlation series can be approximated as universal multifractals.