Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion

Markus Bibinger, Jun Yu and Chen Zhang

Papers from arXiv.org

Abstract: A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility (RV). We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel method to estimate model parameters, establishing its consistency and asymptotic normality. Additionally, we develop a time-reversibility test, which is typically not rejected by RV 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 this 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 outperforms HAR and its variants in terms of out-of-sample forecast.

Date: 2025-04, Revised 2026-08
New Economics Papers: this item is included in nep-ecm, nep-for and nep-rmg
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Citations: View citations in EconPapers (5)

Published in Journal of Business & Economic Statistics (2026)

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