Parameter estimation of space-time model using genetic algorithm

The Space-Time Autoregressive Moving-Average (STARMA) model family is a statistical inductive model that can be used to describe stationary (or weak stationary) space-time processes. However, parameter estimation of the model often is not easy to obtain analytically because of the hard computation or the unknown probability density function underlying the data. To ease the difficulty, an approach to estimate the parameter is proposed in this study, i.e. genetic algorithm (GA). GA is one of the meta-heuristic methods widely used in many applications including the parameter estimation. The GA is performed through simulations of various combinations of selection and crossover parameter chromosomes. The estimation, then, was carried out by the help of freeware R. The performance of the GA in estimating parameter is measured in the sense of the minimum residual sum of squares and the Akaike Information Criterion (AIC). In order to have a comparable solution, we employed the STARMA model of assault arrests in 14 districts of Northeast Boston (1969-1974) of Pfeifer and Deutsch. The results show that the performance of the GA is relatively competitive to the classical method. Since GA is simple to apply, it might be considered as one of the alternative methods for estimating space-time model parameters.