Abstract: Motivated by modeling and forecasting annual hurricane activity in the North Atlantic, we introduce a class of exponential space-time autoregressive (ESTAR) models for count processes by describing the local characteristics as members of finitely supported exponential families. We show that the joint distribution of a space-time count process conditioned on previous observations is a Gibbs field, and demonstrate that an exponential space-time model can be represented as a finite primitive aperiodic Markov chain. The space-time models are identifiable in the parameter space. Asymptotic properties of the log-likelihood function for the parameters in the processes are investigated. Under mild conditions, the maximum likelihood estimates of the parameters are proved to be consistent and asymptotically normally distributed. In order to solve the intractable-constant problem in the likelihood function, the Maximum Pseudo Likelihood Estimation (MPLE) method and the Markov Chain Monte Carlo Maximum Likelihood (MCML) method are proposed to estimate the parameters in an ESTAR model. Simulation results show that both MPLE and MCML estimates appeared relatively unbiased. The MCML method is preferred primarily due to this method providing reasonable standard error estimates of the estimated parameters.
Key words and phrases: Auto-Poisson process, conditionally specified space-time models, Fisher Information regularity conditions, Hessian matrix, reference and objective functions.