Barunik, J. & Kristoufek, L.: On Hurst exponent estimation under heavy-tailed distributions
| Author(s): | doc. PhDr. Jozef Baruník Ph.D., prof. PhDr. Ladislav Krištoufek Ph.D., |
|---|---|
| Type: | Articles in journals with impact factor |
| Year: | 2010 |
| Number: | 18 |
| ISSN / ISBN: | |
| Published in: | Physica A, 389 (18), pp. 3844-3855 PDF |
| Publishing place: | |
| Keywords: | Hurst exponent, Heavy tails, High frequency data analysis |
| JEL codes: | |
| Suggested Citation: | Barunik J., Kristoufek L. (2010): On Hurst exponent estimation under heavy-tailed distributions, Physica A: Statistical Mechanics and its Applications, 389 (18), pp. 3844-3855 |
| Grants: | 402/09/0965: New Approaches for monitoring and prediction of capital markets GAUK 46108: New Nonlinear Capital Markets Theories: Fractal, Bifurcational and Behavioral Approach GAUK 5183/2010 (118310) Fractality and multi-fractality of financial markets: methods and applications IES Research Framework Institutional task (2005-2011) Integration of the Czech economy into European union and its development |
| Abstract: | In this paper, we show how the sampling properties of the Hurst exponent methods of esti- mation 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 com- parison 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 ex- ponent 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. |
