Asymptotic Properties of Maximum Likelihood Estimates in a Class of Space-Time Regression Models

For statistical analyses of satellite ozone data, Niu and Tiao introduced a class of space-time regression models which took into account temporal and spatial dependence of the observations. In this paper, asymptotic properties of maximum likelihood estimates of parameters in the models are considered. The noise terms in the space-time regression models are in Fact structural periodic vector autoregressive processes. Some properties of the spectral density matrix of the processes are discussed. Under mild conditions, the strong law of large numbers and the central limit theorem for the parameter estimates are proven.