Asymptotic analysis of statistical estimators of parameters for binomial conditionally autoregressive model of spatio-temporal data

Abstract

The binomial conditionally autoregressive model of discrete spatio-temporal data is considered in this paper. This model is a multidimensional inhomogeneous Markov chain with a finite state space. Conditions, under which the binomial conditionally autoregressive model satisfies the ergodic principle, are found in case when exogenous factors depend on time. The maximum likelihood approach is used for statistical estimation of model parameters. It is proved that the constructed maximum likelihood estimators are consistent and asymptotically normal distributed for any bounded values of the model parameters and any bounded values of the exogenous factor in case of statistical identifiability of model parameters. Results of computer experiments on simulated data illustrate consistency of maximum likelihood estimators.

Keywords

• spatio-temporal data
• inhomogeneous markov chain
• ergodic principle
• maximum likelihood estimator
• consistency of estimator
• asymptotic normality