Estimating High Dimensional Multivariate Stochastic Volatility Models
This paper proposes three main results that enable the estimation of high dimensional multivariate stochastic volatility models. The first result is the closed-form steady-state Kalman filter for the multivariate AR(1) plus noise model. The second result is an accelerated EM algorithm for parameters estimation. The third result is an estimator of the correlation of two elliptical random variables with time-varying variances that is consistent and asymptotically normal regardless of the evolution of the variances. Speed and precision of our methodology are evaluated in a simulation experiment. Finally, we implement our method and compare its performance with other approaches in a minimum variance portfolio composed by the constituents of the CAC40 and S&P100 indexes