A1471
Title: Modeling and forecasting realized volatility with multivariate fractional Brownian motion
Authors: Chen Zhang - Sun Yat-sen University (China) [presenting]
Jun Yu - Singapore Management University (Singapore)
Markus Bibinger - University of Wurzburg (Germany)
Abstract: A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. The interplay between correlation coefficients and Hurst exponents is investigated and a novel estimation method for model parameters is proposed, establishing consistency and asymptotic normality of the estimators. Additionally, a time-reversibility test is developed, which is typically not rejected by real volatility data. When the data generating process is a time-reversible mfBm, optimal forecasting formulae are derived and their properties analyzed. 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-based forecasts outperform the scalar HAR, vector HAR and vector HAR with a common factor.
