Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Abstract

We first construct a new generalized Hausman test for detecting the structural change in a multiplicative form of covariance matrix time series model. This generalized Hausman test is asymptotically pivotal, and it has non-trivial power in detecting a broad class of alternatives. Moreover, we propose a new semiparametric covariance matrix time series model, which has a time-varying long run component to take the structural change into account, and a BEKKtype short run component to capture the temporal dependence. A two-step estimation procedure is proposed to estimate this semiparametric model, and the asymptotics of the related estimators are established. Finally, the importance of the generalized Hausman test and the semiparametric model is illustrated by simulations and an application to realized covariance matrix data.1. Introduction. Matrix-variate observations are often encountered in statistical applications with structured information. An important example is the realized covariance (RCOV) matrix, which is calculated from intraday high-frequency returns and able to enhance the prediction ability for the covariance matrix of the underly-Keywords and phrases: Covariance matrix time series model; Profiled quasi maximum likelihood estimation; Realized covariance matrix; Semiparametric time series model; Structural change testing.