Hurst Exponent Calculation Program Guide

To calculate the Hurst exponent, first import the time series data into the program using appropriate data structures (e.g., arrays or pandas DataFrames in Python). Once data ingestion is complete, implement the following computational workflow: Begin by calculating the cumulative deviation range of the time series. This involves computing the mean-adjusted cumulative sum series and determining the difference between maximum and minimum values (R-statistic). Next, partition the time series into logarithmically spaced segments (typically using powers of 2) and calculate the rescaled range (R/S) for each segment size. A key implementation detail involves using numpy's array operations for efficient segmentation and scipy's statistical functions for standard deviation calculations. The final step requires plotting the log(R/S) values against log(segment size) and performing linear regression on the scatter plot. The slope of the best-fit line represents the Hurst exponent, which quantifies long-term memory persistence (H>0.5) or mean-reversion tendency (H<0.5) in time series analysis.