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 πππ~ππΌπ·(π,ππ)
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 πππ~ππΌπ·(π,πΊ)
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%.
Author: Siti Choirun Nisak
Journal Code: jpmatematikagg160033
