Modeling RCOV matrices with a generalized threshold conditional autoregressive Wishart model

摘要

In this article, we propose a generalized threshold conditional autoregressive Wishart (GTCAW) model to analyze the dynamics of the realized covariance (RCOV) matrices. This model extends the idea of [29] to a threshold framework. It is believed that, as in many financial time series, the dynamic of RCOV matrices exhibits nonlinearity and may be better explained by a threshold type model. The noncentrality matrix and scale matrix of the Wishart distribution are piecewise linear driven by the lagged values of RCOV matrices and retain two different sources of dynamics. The GTCAW model guarantees the symmetry and positive definiteness of RCOV matrices, some simulation results on the maximum likelihood estimation are also given. Real data examples based on daily RCOV matrices present the nonlinear behavior in these time series and the usefulness of the proposed model.