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Publication details

On Hurst exponent estimation under heavy-tailed distributions

Journal Article

Baruník Jozef, Krištoufek Ladislav

serial: Physica. A : Statistical Mechanics and its Applications vol.389, 18 (2010), p. 3844-3855

research: CEZ:AV0Z10750506

project(s): 118310, GA UK, GA402/09/0965, GA ČR, 46108, GA UK

keywords: high frequency data analysis, heavy tails, Hurst exponent

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abstract (eng):

In this paper, we show how the sampling properties of Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range anal- ysis (R/S), multifractal detrended fluctuation analysis (MF − DFA), detrending moving average (DMA) and generalized Hurst exponent ap- proach (GHE) estimate Hurst exponent on independent series with dif- ferent 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 Hurst exponent using the different methods. R/S and GHE prove to be robust to heavy tails in the underlying process. GHE provides the low- est variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size.


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Institute of Information Theory and Automation