Fractional Integration and Fat Tails for Realized Covariance Kernels and Returns

We introduce a new fractionally integrated model for covariance matrix dynamics based on the long-memory behavior of daily realized covariance matrix kernels and daily return observations. We account for fat tails in both types of data by appropriate distributional assumptions. The covariance matrix dynamics are formulated as a numerically efficient matrix recursion that ensures positive definiteness under simple parameter constraints. Using intraday stock data over the period 2001-2012, we construct realized covariance kernels and show that the new fractionally integrated model statistically and economically outperforms recent alternatives such as the Multivariate HEAVY model and the 2006 “long-memory” version of the Riskmetrics model.