Vector Autoregressive Generalized Space Time Autoregressive (VAR-GSTAR) Model with 2-Means Clustering on Rainfall of Central Java

Abstract

Monthly interregional rainfall within 29 sub districts/districts of Central Java has big variance.
Because of big variance, it needs clustering. The clustering method is the 2-means clustering. Clustered data
is better than unclustered data. Rainfall data have spatial and temporal effects. Therefore, VAR-GSTAR
model could be applied to monthly rainfall data. VAR-GSTAR model needs a spatial weight to measure
correlation within interregional rainfall. The spatial weight is normalization of cross correlation. VARGSTAR
model has two orders. Autoregressive order is obtained from vector autoregressive (VAR) model
and spatial order is determined from generalized space time autoregressive (GSTAR) model. Because of two
orders, the model could be constructed as VAR-GSTAR (p1) model. The purpose of this research is to apply
VAR-GSTAR model with 2-means clustering on rainfall data within 29 sub districts/districts of Central Java.
The results of this research on rainfall data are VAR-GSTAR (11) model for low cluster and VAR-GSTAR
(21) model for high cluster. VAR-GSTAR (11) has root means square error (RMSE) 173.312 and VARGSTAR
(21) has RMSE 203.272.
Keywords: rainfalls, 2-means clustering, VAR-GSTAR.
INTRODUCTION