Consistency and asymptotic normality of least squares estimators in generalized STAR models

Abstract

Space–time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkovaet al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.