Factor and idiosyncratic VAR volatility matrix models for heavy-tailed high-frequency financial observations

This paper introduces a novel process for both factor and idiosyncratic volatility matrices whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR (FIVAR) model. The FIVAR model accounts for the dynamics of the factor and idiosyncratic volatilities and includes many parameters. In addition, many empirical studies have shown that high-frequency stock returns and volatilities often exhibit heavy tails. To handle these two problems simultaneously, we propose a penalized optimization procedure with a truncation scheme for parameter estimation. We apply the proposed parameter estimation procedure to predicting large volatility matrices and establish its asymptotic properties.