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

Abstract

Multifractal Detrended Fluctuation Analysis (MFDFA) is an efficient method to investigate the long-term correlations of the power law of non-stationary time series, in which the elimination of local trends usually depends upon a fixed-constant polynomial order. In this paper, we propose a flexible set of polynomial and trigonometric functions to better detect, and correctly model, hidden local trends in the time series at different scales. We introduce the Multifractal Detrended Fluctuation Analysis with Polynomial and Trigonometric functions (MFDFAPT) method via optimal model selection from an optimization framework. The performance of MFDFAPT is assessed with extensive numerical experiments based on the multifractal binomial cascade process, fractional Brownian movements, and fractional Gaussian noises. MFDFAPT shows better performance than MFDFA in the approximation of the Hurst index, and correctly determines the scalar behavior in stationary and non-stationary series. Additionally we apply MFDFAPT to detect and characterize the scalar properties of the daily precipitation time series in meteorological stations of Tabasco, México. Our results confirm previous indications that the general Hurst exponent depends on the physiographic characteristics of the study area, and that fractal dimension correctly characterizes the series of daily precipitations in tropical regions.