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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Bayesian estimation of self-similarity exponent.

Natallia Makarava¹, Sabah Benmehdi, Matthias Holschneider

¹University of Potsdam, Interdisciplinary Center for Dynamics of Complex Systems, Karl-Liebknecht-Strasse 24, D-14476 Potsdam, Germany.

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Summary

This study introduces a Bayesian method using linear mixed models for estimating the Hurst exponent, effective even with incomplete data. The approach accurately analyzes complex time series, including financial data like the Dow Jones Industrial Average.

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Area of Science:

Time Series Analysis
Statistical Modeling
Stochastic Processes

Background:

The Hurst exponent is a key measure of long-term memory in time series.
Estimating the Hurst exponent is challenging for unevenly sampled data or data with gaps.
Existing methods may not be robust to these data imperfections.

Purpose of the Study:

To develop a robust Bayesian approach for Hurst exponent estimation.
To demonstrate the method's applicability to various data types, including financial markets.
To provide a reliable tool for analyzing self-similar processes.

Main Methods:

Utilized a Bayesian framework with linear mixed models.
Applied the method to artificial Fractional Brownian Motion and Rosenblatt processes.
Compared performance against Detrended Fluctuation Analysis.
Analyzed real-world financial data (Dow Jones Industrial Average).

Main Results:

The proposed Bayesian method accurately estimates the Hurst exponent for various signal types.
The method is effective even with unevenly sampled data and data containing gaps.
Demonstrated successful application to H-self-similar processes with non-Gaussian distributions.
Revealed temporal variations in the Hurst exponent for the Dow Jones Industrial Average.

Conclusions:

The Bayesian linear mixed model approach offers a powerful and flexible tool for Hurst exponent estimation.
This method enhances the analysis of complex and real-world time series data.
The findings have implications for understanding memory and scaling properties in diverse fields.