Semiparametric model for covariance regression analysis

Estimating covariance matrices is an important research topic in statistics and finance. A semiparametric model for covariance matrix estimation is proposed. Specifically, the covariance matrix is modeled as a polynomial function of the symmetric adjacency matrix with time varying parameters. The asymptotic properties for the time varying coefficient and the associated semiparametric covariance estimators are established. A Bayesian information criterion to select the order of the polynomial function is also investigated. Simulation studies and an empirical example are presented to illustrate the usefulness of the proposed method.