Pengembangan Model Spatio Temporal dan Aplikasinya

Budi Nurani Ruchjana


Spatio Temporal or Space Time Model is a stochastic processes which indexed by space and time simultaneously. In this paper we studied a development of spatio temporal model especially in Generalized Spatio temporal Autoregressive (GSTAR) model which is developed from Spatio temporal Autoregressive (STAR) model from Pfeifer (1979). STAR and GSTAR models are developed as a univariate time series from Box-Jenkins (1976). GSTAR model is a stationary multivariate time series model, which has an assumption that parameters are vary per location, so it is capable for heterogenous locations characteristic. GSTAR model can be applied for forecasting an observation at the future time based on lag time before and influenced by the observations at surrounding locations. For example of GSTAR model can be used in forecasting of oil production at oil wells at volcanic field Jatibarang, forcasting of tea productivities at several plantations in West Java and forecasting of rainfall at West Java area etc. The stationary GSTAR model can be extend to be GSTAR-X with addition of exogeneous variable, or to be non-stationary model as GSTARI or GSTAR-ARCH and KSTAR-Kriging. To make easier in estimaton of parameters of GSTAR model , we built an interactive software using the script of opensource R software using Ordinary Least Squares (OLS) method.  Spatio Temporal Model especially the GSTAR model can be used for recommendation of management in decision making at a certain area.


spatio temporal model, GSTAR, GSTAR-X, GSTARI, GSTAR-ARCH, OLS

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Armstrong, M, (1998), Basic Linear on Geostatistics, New York: Springer Verlag.

Borovkova, Lopuhaa, and Ruchjana, B.N., (2008), Consistency and Asymtotic Normality of Least Squares Estimators in Generalized STAR Models, Statistica Neerlandica, vol. 62, issue 4, p. 482-508.

Box, G.E.P. and Jenkins, G.M., (1976), Time Series Analysis, Forecasting and Control, Holden-Day, Inc., San Fransisco.

Cliff, A.D. and Ord, K., (1975), Model building and the analysis of spatial pattern in human geography, J. Roy. Statist. Soc. B, Vol. 37, p. 297-348.

Elfiyan, I. (2015). Penerapan Model GSTARI-X pada data Banyaknya Peserta KB Aktif di Jawa Barat.

Hannan, E.J. , (1970), Multiple Time Series, John Wiley and Sons, Inc., New York.

Hanin, T. 2014. Pemodelan Generalized Space Time Autoregressive (GSTARI) Pada Data Curah Hujan. Malang: Jurusan Matematika Universitas Brawijaya.

Pfeifer, P. E. , (1979), Spatial-Dynamic Modeling, unpublished-Dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta-Georgia

Ruchjana, B. N. (2002), Suatu Model Generalisasi Spatio temporal Autoregresi dan Penerapannya pada Produksi Minyak Bumi. Disertasi S3 tidak dipublikasikan, Bandung: PPs ITB.

Ruchjana, B. N. dan Darwis, S. (2005). Oil Well Placement using the GSTAR-Kriging Model, Open Science Meeting at Yogyakarta, Funding by KNAW the Netherlands.

Wei, W. (1990), Time Series Univariate and Multrivariat Method.son-Wesley Publishing Company, Inc., New

Ruchjana, B.N. dkk. (2005). Studi Pengembangan Model Spatio Temporal dan Aplikasinya Dalam Lingkungan Hidup,Pustaka Ilmiah, Universitas Padjadjaran, Bandung.

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