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A guide to Whittle maximum likelihood estimator in MATLAB.

Clément Roume¹

¹IRIMAS UR UHA 7499, University of Haute-Alsace, Mulhouse, France.

Frontiers in Network Physiology

|November 29, 2023

Summary

This summary is machine-generated.

This tutorial introduces Whittle's maximum likelihood estimator (MLE) for analyzing physiological complexity in biological signals. This method offers a simpler, more accurate way to estimate monofractal exponents from shorter time series data.

Keywords:

ARFIMA (0,d,0)Whittle’s likelihood fractals fractional Gaussian noise tutorial

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Area of Science:

Physiology
Complexity Science
Signal Processing

Background:

Assessing physiological complexity using fractal analysis of biological signals is an emerging research area.
Monofractal exponents and multifractal spectra provide insights into health, learning, and autonomy.
Existing methods for monofractal analysis often require long time series.

Purpose of the Study:

To introduce Whittle's maximum likelihood estimator (MLE) for estimating the monofractal exponent of time series.
To present the steps involved in constructing the Whittle's MLE algorithm.
To compare the performance of Whittle's MLE with the detrended fluctuation analysis (DFA).

Main Methods:

Whittle's maximum likelihood estimator (MLE) for monofractal exponent estimation.
Algorithm construction for Whittle's MLE.
Comparative analysis against detrended fluctuation analysis (DFA).

Main Results:

Whittle's MLE is a viable alternative for monofractal exponent estimation.
The method is simpler to implement compared to existing techniques.
Whittle's MLE demonstrates high accuracy, enabling analysis of shorter time series.

Conclusions:

Whittle's MLE offers an accessible and accurate approach to analyzing physiological complexity.
This method expands the applicability of monofractal analysis to shorter biological signals.
The tutorial provides a foundation for researchers to utilize this advanced signal processing technique.