Correlation in space and in time is a common phenomenon among biological and environmental processes. However, in space-time ARMA modeling which is a widely used modeling for space-time correlated process, there exist some difficulties in the modeling procedure, that have impeded practical applications since the statistical theory was developed. The difficulties include no robust optimization algorithm and no appropriate criteria for space-time model evaluation. In this paper, a space-time extension of Hannan-Rissanen algorithm is suggested for accelerating the modeling process and improving robustness while optimizing model parameters. This study makes the space-time modeling practical.