Which Methods Perform Better for Real-Time Hurst Parameter Estimation?

Long-range dependence (LRD) in complex time series is becoming an increasingly important aspect in the era of big data as we explore further into the complex world. From natural processes like heart rate variability (HRV) or manmade systems like the stock market, LRD is omnipresent. As such, accurately characterizing the LRD in terms of the Hurst parameter in these complex time series generated from complex systems is important. Most existing methods for Hurst parameter estimation are for batch or offline processing. To achieve real-time evaluation, a moving window approach is applied when quantifying the LRD in the time series. This paper focuses on evaluating various techniques that estimate the Hurst parameter embedded in the LRD time series. Nine techniques were analyzed, and three were determined to be the most accurate: Higuchi's method, Diffusion Entropy Analysis, and Detrended Fluctuation Analysis for online real-time estimation of Hurst parameters. All reported results are reproducible for further robustness evaluation of online real-time Hurst parameter estimation.