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

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  • Matthieu Garcin

    (Natixis Asset Management, Labex ReFi - UP1 - Université Paris 1 Panthéon-Sorbonne)

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-varying 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.

Suggested Citation

  • Matthieu Garcin, 2016. "Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates," Working Papers hal-01399570, HAL.
    • Handle: RePEc:hal:wpaper:hal-01399570
    Note: View the original document on HAL open archive server: https://hal.science/hal-01399570
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    Cited by:

    1. Matthieu Garcin & Clément Goulet, 2015. "Non-parameteric news impact curve: a variational approach," Documents de travail du Centre d'Economie de la Sorbonne 15086rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Feb 2017.

    More about this item

    Keywords

    Hurst exponent; Euler-Lagrange equation; non-parametric smoothing; foreign exchange forecast; Multifractional brownian motion;
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