Sequential estimation of multivariate factor stochastic volatility models

Abstract

We provide the first “frequentist” method to estimate the parameters of multivariate stochastic volatility models with latent factor structures to capture the time-varying variance–covariance of financial returns. These models alleviate the standard curse of dimensionality, allowing the number of parameters to increase only linearly with the number of series. Although theoretically very appealing, they have only found limited practical application due to huge computational burdens. Our estimation method is simple in implementation as it consists of two steps: first, we estimate the loadings and the unconditional variances by maximum likelihood, and then, we use the efficient method of moments to estimate the parameters of the stochastic volatility structure with the generalised autoregressive conditional heteroskedasticity (GARCH) auxiliary models. In a comprehensive Monte Carlo study, we show the good performance of our method to estimate the parameters of interest accurately. The simulation study and an application to the daily returns on 148 stocks in the cross-sectional dimension provide sound evidence on the computational feasibility of the method proposed and its application.