Realized BEKK-CAW Models

Estimating time-varying conditional covariance matrices of financial returns play important role in portfolio analysis, risk management, and financial econometrics research. The availability of high-frequency financial data can provide an additional data source for dynamic covariance modeling. In this paper, we propose to use the information of asset return vector and realized covariance measures simultaneously to develop a new conditional covariance matrix model. We derive the stationary condition of the new model. We use the normal and Wishart distributions to construct the quasi-log-likelihood function. We also consider the variance targeting (VT) method, which plugs in the weighted average of the sample covariance matrix of returns and the sample mean of realized covariance measure for the unconditional covariance matrix, in order to maximize the quasi-log-likelihood function. We show the consistency and asymptotic normality of the quasi-maximum likelihood (QML) and VT estimators. We investigate the finite sample property of these estimators via Monte Carlo experiments. The empirical example for the bivariate data of the Nikkei 225 index and its futures indicates that the first-step VT estimation could have non-negligible effects on the standard errors of the second-step VT estimates.