On Hurst exponent estimation under heavy-tailed distributions
By Jozef Baruník, Ladislav Kristoufek. 2010
272 citations recorded by the source corpus.
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.
Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2a2d220fd170dca10d3bf213de21383cd31baa30
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
- Ladislav Kristoufek
- Miloslav S. Vosvrda
- T. Di Matteo
- Raffaello Morales
- Ruggero Gramatica
- Tomaso Aste
- Matthieu Garcin
- Ayoub Ammy-Driss
In Finance
- Ladislav Kristoufek
- Miloslav S. Vosvrda
- T. Di Matteo
- Raffaello Morales
- Ruggero Gramatica
- Tomaso Aste
- Ayoub Ammy-Driss
- Matthieu Garcin
In Statistical and Nonlinear Physics
- Ladislav Kristoufek
- Miloslav S. Vosvrda
- T. Di Matteo
- Tomaso Aste
- Raffaello Morales
- Ruggero Gramatica
- Raphael Heiko Heiberger
- Gangjin Wang
Citations in the corpus
- Measuring capital market efficiency: Global and local correlations structure (2012, methodology): “Such a procedure is chosen because each of the methods is better suited for different types of processes both for Hurst exponent and fractal dimension estimation [46, 7, 30, 25].”
- Commodity futures and market efficiency (2013, methodology): “h time and frequency domain estimators, see Beran (1994); Taqqu et al. (1995); Taqqu and Teverovsky (1996); Robinson (1995); Geweke and Porter-Hudak (1983); Di Matteo et al. (2003); Di Matteo (2007); Barunik and Kristoufek (2010); Teverovsky et al. (1999). Out of theses estimators, we opt for the lo”
- Mixed-correlated ARFIMA processes for power-law cross-correlations (2013, background): “Long-term memory has been studied for stock indices [11, 12, 7, 19, 18], bonds [9, 12], exchange rates [39, 25], commodities [2, 3, 31], interest rates [8, 10] and others.”
- Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series (2011, methodology): “Although multi-scaling analysis based on the GHE has been already extensively pursued in the literature [9, 10, 11, 14, 15, 16, 17, 18, 19, 20], the dynamics of the GHE has been scarcely investigated [21].”