Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall Data in Malang Southern Region Districts

Abstract

Time series forecasting models can be used to predict phenomena that occur in nature. Generalized Space Time Autoregressive (GSTAR) is one of time series model used to forecast the data consisting the elements of time and space. This model is limited to the stationary and non-seasonal data. Generalized Space Time Autoregressive Integrated Moving Average (GSTARIMA) is GSTAR development model that accommodates the non-stationary and seasonal data. Ordinary Least Squares (OLS) is method used to estimate parameter of GSTARIMA model. Estimation parameter of GSTARIMA model using OLS will not produce efficiently estimator if there is an error correlation between spaces. Ordinary Least Square (OLS) assumes the variance-covariance matrix has a constant error 𝜀𝑖𝑗~𝑁𝐼𝐷(𝟎,𝝈𝟐) but in fact, the observatory spaces are correlated so that variance-covariance matrix of the error is not constant. Therefore, Seemingly Unrelated Regression (SUR) approach is used to accommodate the weakness of the OLS. SUR assumption is 𝜀𝑖𝑗~𝑁𝐼𝐷(𝟎,𝚺) for estimating parameters GSTARIMA model. The method to estimate parameter of SUR is Generalized Least Square (GLS). Applications GSTARIMA-SUR models for rainfall data in the region Malang obtained GSTARIMA models ((1)(1,12,36),(0),(1))-SUR with determination coefficient generated with the average of 57.726%.