Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion
Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion
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.
Markus Bibinger、Jun Yu、Chen Zhang
数学计算技术、计算机技术
Markus Bibinger,Jun Yu,Chen Zhang.Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion[EB/OL].(2025-04-22)[2025-05-17].https://arxiv.org/abs/2504.15985.点此复制
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