Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates

Matthieu Garcin

Physica A: Statistical Mechanics and its Applications, 2017, vol. 483, issue C, 462-479

Abstract: Hurst exponents depict the long memory of a time series. For human-dependent phenomena, as in finance, this feature may vary in the time. It justifies modelling dynamics by multifractional Brownian motions, which are consistent with time-dependent Hurst exponents. We improve the existing literature on estimating time-dependent Hurst exponents by proposing a smooth estimate obtained by variational calculus. This method is very general and not restricted to the sole Hurst framework. It is globally more accurate and easier than other existing non-parametric estimation techniques. Besides, in the field of Hurst exponents, it makes it possible to make forecasts based on the estimated multifractional Brownian motion. The application to high-frequency foreign exchange markets (GBP, CHF, SEK, USD, CAD, AUD, JPY, CNY and SGD, all against EUR) shows significantly good forecasts. When the Hurst exponent is higher than 0.5, what depicts a long-memory feature, the accuracy is higher.

Keywords: Multifractional Brownian motion; Hurst exponent; Euler–Lagrange equation; Non-parametric smoothing; Foreign exchange forecast (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (35)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:483:y:2017:i:c:p:462-479

DOI: 10.1016/j.physa.2017.04.122

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