Covariance matrix and transfer function of dynamic generalized linear models

Statistical inference for dynamic generalized linear models (DGLMs) is challenging due to the time varying nature of the unknown parameters in these models. In this paper, we focus on the covariance matrix and the transfer function, the two key components in DGLMs. We first establish some convergence results for the covariance matrix estimation. We then provide an in-depth study of the transfer function on its stability and Fourier transformation, which is necessary for parameter estimation in DGLMs. Implications of our results on estimation in DGLMs are illustrated in the paper through a simulation study and a real data example. Our understanding on DGLMs has substantially improved though this study.