A Time Series Model for Realized Volatility Matrices Based on the Matrix-F Distribution

Abstract

Realized covariance (RCOV), as a volatility estimator calculated from high frequency time series, is playing an important role in recent statistics and econometrics researches. We focus on modeling the dynamic of the stochastic, symmetric and positive definite RCOV matrices. Unlike some pioneer works in this field, including WAR or CAW models where the Wishart distribution is adopted, we suggest the utilization of a more general matrix-F distribution, to accommodate heavy-tailed data. We managed to provide sufficient condition for the stationarity of the model. Concerning the curse of dimensionality and over-parametrization problems, under stationarity, a parsimonious variance targeted (VT) model is introduced. Under this VT setting, the asymptotic consistency and normality of the maximum likelihood estimator are established. Moreover, this VT model is further reduced to parsimonious forms, with merits on maintaining positive definiteness and computation flexibility. Monte Carlo simulations are used for demonstrating the methodology and real data analysis is conducted on intraday data from S&P500 database.