Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion

Markus Bibinger, Jun Yu and Chen Zhang
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Markus Bibinger: Faculty of Mathematics and Computer Science, Institute of Mathematics, University of Würzburg
Chen Zhang: Faculty of Business Administration, University of Macau

No 202528, Working Papers from University of Macau, Faculty of Business Administration

Abstract: A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel estimation method for all model parameters, establishing consistency and asymptotic normality of the estimators. Additionally, we develop a time-reversibility test, which is typically not rejected by real volatility data. When the data-generating process is a time-reversible mfBm, we derive optimal forecasting formulae and analyze their properties. A key insight is that an mfBm with different Hurst exponents and non-zero correlations can reduce forecasting errors compared to a one-dimensional model. Consistent with optimal forecasting theory, out-of-sample forecasts using the time-reversible mfBm show improvements over univariate fBm, particularly when the estimated Hurst exponents differ significantly. Empirical results demonstrate that mfBm-based forecasts outperform the (vector) HAR model.

Keywords: Forecasting; Hurst exponent; multivariate fractional Brownian motion; realized volatility; rough volatility (search for similar items in EconPapers)
JEL-codes: C12 C58 (search for similar items in EconPapers)
Pages: 60 pages
Date: 2025-04
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-rmg
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Published in UM-FBA Working Paper Series

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Related works:
Working Paper: Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion (2025)
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