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Abstract:
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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 non-asymptotic convergence rates for estimating the latent processes of factors and their loadings, we further study the 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 asymp
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