A guide to Whittle maximum likelihood estimator in MATLAB

Abstract

The assessment of physiological complexity via the estimation of monofractal exponents or multifractal spectra of biological signals is a recent field of research that allows detection of relevant and original information for health, learning, or autonomy preservation. This tutorial aims at introducing Whittle’s maximum likelihood estimator (MLE) that estimates the monofractal exponent of time series. After introducing Whittle’s maximum likelihood estimator and presenting each of the steps leading to the construction of the algorithm, this tutorial discusses the performance of this estimator by comparing it to the widely used detrended fluctuation analysis (DFA). The objective of this tutorial is to propose to the reader an alternative monofractal estimation method, which has the advantage of being simple to implement, and whose high accuracy allows the analysis of shorter time series than those classically used with other monofractal analysis methods.