Wen Zhou, PhD

"Estimation and Interence of Heteroskedasticity Models with Latent Semiparametric Factors for Multivariate Time Series"

Abstract: This paper considers estimation and inference of a flexible heteroskedasticity model for multivariate time series, which employs semiparametric latent factors to simultaneously account for the heteroskedasticity and contemporaneous correlations. Specifically, the heteroskedasticity is modeled by the product of unobserved stationary processes of factors and subject-specific covariate effects. Serving as the loadings, the covariate effects are further modeled through additive models. We propose a two-step procedure for estimation. First, the latent processes of factors and their nonparametric loadings are estimated via projection-based methods. The estimation of regression coefficients is further conducted through generalized least squares. Theoretical validity of the two-step procedure is documented. By carefully examining the convergence rates for estimating the latent processes of factors and their loadings, we further study the asymptotic properties of the estimated regression coefficients. In particular, we establish the asymptotic normality of the proposed two-step estimates of regression coefficients. The proposed regression coefficient estimator is also shown to be asymptotically efficient. This leads us to a more efficient confidence set of the regression coefficients. Using an comprehensive simulation study, we demonstrate the finite sample performance of the proposed procedure, and numerical results corroborate our theoretical findings. Finally, we illustrate the use of our proposal to study the US air quality data and report interesting finding.

Bio: Wen Zhou, Ph.D., is an Assistant Professor in the Department of Statistics at Colorado State University. He obtained his Ph.D. degrees in Applied Mathematics and Statistics at Iowa State University. Dr. Zhou’s research mainly focuses on high dimensional inference, statistical machine learning, mathematical statistics, time series, statistical genomics and genetics, and computational biology.