Optimizing a Bayesian method for estimating the Hurst exponent in behavioral sciences

Abstract

The Bayesian Hurst-Kolmogorov (HK) method estimates the Hurst exponent of a time series more accurately than the age-old detrended fluctuation analysis (DFA), especially when the time series is short. However, this advantage comes at the cost of computation time. The computation time increases exponentially with N, easily exceeding several hours for N = 1024, limiting the utility of the HK method in real-time paradigms, such as biofeedback and brain-computer interfaces. To address this issue, we have provided data on the estimation accuracy of H for synthetic time series as a function of a priori known values of H, the time series length, and the simulated sample size from the posterior distribution -- a critical step in the Bayesian estimation method. The simulated sample from the posterior distribution as small as n = 25 suffices to estimate H with reasonable accuracy for a time series as short as 256 measurements. Using a larger simulated sample from the posterior distribution -- i.e., n > 50 -- provides only marginal gain in accuracy, which might not be worth trading off with computational efficiency. We suggest balancing the simulated sample size from the posterior distribution of H with the computational resources available to the user, preferring a minimum of n = 50 and opting for larger sample sizes based on time and resource constraints

Tasks

Reproductions