A New Semiparametric Estimation Approach of Large Dynamic Covariance Matrices with Multiple Conditioning Variables

This paper studies the estimation of dynamic covariance matrices with multiple conditioning variables, where the matrix size can be ultra large (divergent at an exponential rate of the sample size). We introduce an easy-to-implement semiparametric method to estimate each entry of the covariance matrix via model averaging marginal regression, and then apply a shrinkage technique to obtain the large dynamic covariance matrix estimation. Under some regularity conditions, we derive the asymptotic properties for the proposed estimators including the uniform consistency with general convergence rates. We further consider extending our methodology to deal with the scenarios: (i) the number of conditioning variables is divergent as the sample size increases, and (ii) the large covariance matrix is conditionally sparse relative to contemporaneous market factors. We provide a simulation study that illustrates the finite-sample performance of the developed methodology. We also provide an application to financial portfolio choice from daily stock returns