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Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

Buonocore, RJ; Aste, T; Di Matteo, T; (2017) Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data. Physical Review E , 95 , Article 042311. 10.1103/PhysRevE.95.042311. Green open access

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Abstract

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

Type: Article
Title: Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevE.95.042311
Publisher version: http://doi.org/10.1103/PhysRevE.95.042311
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Physics, Fluids & Plasmas, Physics, Mathematical, Physics, DETRENDED FLUCTUATION ANALYSIS, SWITCHING MULTIFRACTAL MODEL, ASSET RETURNS, TIME-SERIES, MARKETS, VOLATILITY, COMPONENTS, TURBULENCE, FRACTALS, MEMORY
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1572210
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