The Minimum Number of Observations in Space Time Autoregressive Modeling Utriweni Mukhaiyar
Statistics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Abstract
In accordance with the Weak Law of Large Number that the larger the size of observations, the closer the value of the parameter estimator its true value. But taking a large sample size is not an effective and efficient solution in modeling. This also applies to time series and space time modeling, A minimum reference value for the number of observations time is required, in order to obtain the appropriate model which is closer to the real model. In this research, the minimum number of observations is determined through the Monte-Carlo simulation for the Generalized Space Time Autoregressive (GSTAR) model. The criteria used are that the difference between the estimator and the true parameter for all observed locations are smaller than a small real value. It is complying with the principle of convergence in probability, that is the greater sample size then the smaller the errors. It is obtained that the smaller the time order of GSTAR model, the smaller the number of observations time is required. The closer the process to be a nonstationary, the longer the amount of observations time.
Keywords: minimum number of time, GSTAR model, stationary, error, convergence
