Simple Hurst Exponent Calculation with MATLAB Implementation

This article demonstrates how to create a MATLAB program to calculate the Hurst exponent. First, we need to understand what the Hurst exponent represents and its practical applications. The Hurst exponent is a statistical measure used to quantify the long-term memory and persistence in time series data, commonly applied in analyzing financial market volatility. The implementation involves several key MATLAB functions and computational steps: data reading functions like readtable or xlsread for importing financial time series, mean calculation using mean function, standard deviation computation with std, and rescaled range analysis algorithm implementation. The core algorithm calculates the R/S statistic by dividing the time series into multiple windows, computing the range of cumulative deviations normalized by the standard deviation for each window. For this program, we'll apply the Hurst exponent to analyze stock market volatility patterns. The implementation requires basic MATLAB operations including data preprocessing, logarithmic returns calculation, and iterative computation across different time scales. After completing the program, we'll conduct testing using historical stock data and discuss the interpretation of results. Through the methodology presented in this article, readers will learn how to implement a straightforward Hurst exponent calculation program in MATLAB and apply it to volatility analysis in financial markets. The program structure includes data input validation, algorithm parameter configuration, and result visualization components.