Blocks adjustment -- reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation

TL;DR

This paper investigates how block length choices affect bias and variance in Detrended Fluctuation Analysis (DFA) and proposes optimal block ranges through extensive Monte Carlo simulations to improve Hurst exponent estimation.

Contribution

It introduces an optimized block selection method for DFA based on simulation results, reducing bias and variance in Hurst exponent estimation.

Findings

Optimal block pairs minimize mean-squared error in Hurst estimation.

DFA sensitivity varies with series correlation structure.

Bias correction improves anti-persistent process analysis.

Abstract

The length of minimal and maximal blocks equally distant on log-log scale versus fluctuation function considerably influences bias and variance of DFA. Through a number of extensive Monte Carlo simulations and different fractional Brownian motion/fractional Gaussian noise generators, we found the pair of minimal and maximal blocks that minimizes the sum of mean-squared error of estimated Hurst exponents for the series of length N=2^p, p=7,...,15. Sensitivity of DFA to sort-range correlations was examined using ARFIMA(p,d,q) generator. Due to the bias of the estimator for anti-persistent processes, we narrowed down the range of Hurst exponent to 1/2<=H< 1.