Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1201.4786

On Hurst exponent estimation under heavy-tailed distributions

Jozef Barunik·Ladislav Kristoufek
View original source ↗Read source document ↗Export metadata ↓

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 α 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.

Explore related subjects

q-fin.ST

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jozef Barunik, Ladislav Kristoufek. 2012-01-23. On Hurst exponent estimation under heavy-tailed distributions. https://doi.org/10.1016/j.physa.2010.05.025

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Causal Discovery in Financial Markets: A Framework for Nonstationary Time-Series Data

This paper introduces a new causal structure learning method for nonstationary time series data, a common data type found in fields such as finance, economics, healthcare, and environmental science. Our work builds upon the constraint-based causal discovery from nonstationary data algorithm (CD-NOD). We introduce a refined version (CDNOTS) which is designed specifically to account for lagged dependencies in time series data. We compare the performance of different algorithmic choices, such as the type of conditional independence test and the significance level, to help select the best hyperparameters given various scenarios of sample size, problem dimensionality, and availability of computational resources. Using the results from the simulated data, we apply CDNOTS to a broad range of real-world financial applications in order to identify causal connections among nonstationary time series data, thereby illustrating applications in factor-based investing, portfolio diversification, and comprehension of market dynamics.

q-fin.ST↗
arXiv2026

Extreme Value Analysis for Finite, Multivariate and Correlated Systems with Finance as an Example

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value analysis for infinite correlated systems remains an open challenge, we propose a practical framework for handling a large but finite number of correlated time series. We develop our approach for finance as a concrete example but emphasize its generality. We study the extremal behavior of high-frequency stock returns after rotating them into the eigenbasis of the correlation matrix. This separates and extracts various collective effects, including information on the correlated market as a whole and on correlated sectoral behavior from idiosyncratic features, while allowing us to use univariate tools of extreme value analysis. This holds even for high-frequency data where discretization effects normally complicate analysis. We employ a peaks-over-threshold approach and thereby fully avoid the analysis of block maxima. We estimate the tail shape of the rotated returns while explicitly accounting for nonstationarity, a key feature in finance and many other complex systems. Our framework facilitates tail risk estimation relative to larger trends and intraday seasonalities at both market and sectoral levels.

q-fin.ST↗
arXiv2026

Does Crypto Sentiment Extremity Widen Estimated Spreads? Evidence Depends on the Specification

We examine whether extreme values of the Crypto Fear & Greed Index are associated with a daily high-low spread estimate for Bitcoin. The sample contains 2,896 BTC/USDT observations from February 2018 to January 2026. We find an unconditional extreme-minus-neutral gap of 61.99 basis points. After close-to-close realised-volatility-quintile demeaning it is 24.79 basis points, although none of the five separate quintile contrasts survives Holm correction. With quadratic realised-volatility and strictly lagged momentum controls, the HAC estimate is 11.81 basis points (95% CI [-2.31,25.93], p=.101). A fixed non-parametric stratification gives 20.44 basis points (p=.0195 under circular shifts), while separate models for a zero-floored estimate's incidence and positive magnitude are imprecise. The results therefore show only a descriptive, specification-dependent association. We conclude that they do not establish a stable or causal liquidity premium.

q-fin.ST↗