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01-Applied Mathematics & Information Sciences
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Volumes > Volume 12 > No. 3

 
   

Implementation of Generalized Space Time Autoregressive (GSTAR)-Kriging Model for Predicting Rainfall Data at Unobserved Locations in West Java

PP: 607-615
doi:10.18576/amis/120316
Author(s)
Atje Setiawan Abdullah, Setiawan Matoha, Deltha Airuzsh Lubis, Annisa Nur Falah, I. G. N. Mindra Jaya, Eddy Hermawan, Budi Nurani Ruchjana,
Abstract
A Generalized Space Time Autoregressive or GSTAR is a special model of Vector Autoregressive (VAR) model which is a combination of time series and spatial models which has the assumption of autoregressive parameter and space time parameter having different value for each location of observation. In addition, it assumes stationary time series data at the mean and variance levels and applies to locations with heterogeneous characteristics. One disadvantage of the GSTAR model is that it can not be used to predict at unobserved locations. In this paper we combine the GSTAR model with the Ordinary Kriging (OK) technique, named GSTAR-Kriging model so that the GSTAR model can be used to predict in unobserved locations. GSTAR parameters are estimated using the Ordinary Least Squares (OLS) method and these are used as inputs for the Kriging technique. Furthermore, by using linear semivariogram we can obtain simulations to predict the GSTAR parameters. For the case study we applied the model to annual rainfall data in wet season (Desember, January and February) from several locations in West Java, Indonesia, such as Majalengka, Kuningan and Ciamis Regencies. The GSTAR (1;1) model in observed location have Mean Average Percentage Error (MAPE) value overall less than 15 percent and residual of model have identically independent distributed normal. The results of GSTAR-Kriging model show that the GSTAR-Kriging parameter at unobserved locations are almost similar to GSTAR parameter at observed locations.

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