On Hurst exponent estimation under heavy-tailed distributions

TL;DR

This study evaluates how different Hurst exponent estimation methods perform under heavy-tailed distributions, finding GHE to be the most robust and least biased, and applies this to analyze intraday market behavior over decades.

Contribution

It introduces a comprehensive comparison of Hurst exponent estimation methods under heavy tails and proposes a novel intraday time-dependent Hurst analysis for financial data.

Findings

GHE has lowest bias and variance across heavy tails

R/S and GHE are robust to heavy tails

Market behavior changed significantly over the studied period

Abstract

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on independent series with different heavy tails. For this purpose, we generate independent random series from stable distribution with stability exponent {\alpha} changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution) and we estimate the Hurst exponent using the different methods. R/S and GHE prove to be robust to heavy tails in the underlying process. GHE provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size. Utilizing this result, we apply a novel approach of the intraday time-dependent Hurst exponent and we estimate the Hurst exponent on high frequency data for each trading day separately. We obtain Hurst exponents for S&P500 index for the period beginning with year 1983 and ending by November 2009 and we discuss the surprising result which uncovers how the market's behavior changed over this long period.