Analysis of Generalized Space Time Autoregressive with Exogenous Variable (GSTARX) Model with Outlier Factor

Abstract

The outlier is an observation data that has different characteristics from others. Frequently, outliers are removed to improve the accuracy of the estimators. But sometimes the presence of an outlier has a specific meaning, which explanation can be lost if the outlier is removed. There are two exceptional cases from types of outliers, Innovative Outlier (IO) and Additive Outlier (AO). The presence of an outlier in the space-time model is no exception. Space-time model, not only influenced by previous observations at the same location and previous observations in a different location, or there are not only time and location dependencies, but also there are some other things that affect, which can be expressed as an exogenous variable. GSTARX is a model that combines not only time and location but also involves exogenous variables. In the GSTARX model, the presence of outliers may also be detected and may have spatial correlation at a time. In this paper, the iterative procedure in detecting outliers in the GSTARX model was introduced. Therefore data containing outliers is not deleted or ignored but still involves the outlier data by adding an outlier factor to the GSTARX model. The power of the procedure in detecting outliers is investigated by simulation experiments. The result is a GSTARX model with outlier factors that maintain the outlier factor.