Cross-Covariance Weight of GSTAR-SUR Model for Rainfall Forecasting in Agricultural Areas

Agus Dwi Sulistyono, Hartawati Hartawati, Ni Wayan Suryawardhani, Atiek Iriany, Aniek Iriany


The use of location weights on the formation of the spatio-temporal  model contributes to the accuracy of the model formed. The location weights that are often used include uniform location weight, inverse distance, and cross-correlation normalization. The weight of the location considers the proximity between locations. For data that has a high level of variability, the use of the location weights mentioned above is less relevant. This research was conducted with the aim of obtaining a weighting method that is more suitable for data with high variability. This research was conducted using secondary data derived from 10 daily rainfall data obtained from BMKG Karangploso. The data period used was January 2008 to December 2018. The points of the rain posts studied included the rain post of the Blimbing, Karangploso, Singosari, Dau, and Wagir regions. Based on the results of the research forecasting model obtained is the GSTAR ((1), 1,2,3,12,36) -SUR model. The cross-covariance model produces a better level of accuracy in terms of lower RMSE values and higher R2 values, especially for Karangploso, Dau, and Wagir areas.


cross-covariance; GSTAR Model; rainfall; spatio-temporal

Full Text:



P. E. Pfeifer and S. J. Deutsch, “Identification and interpretation of first order space-time arma models,” Technometrics, 1980.

P. E. Pfeifer and S. J. Deutsch, “Seasonal Space‐Time ARIMA Modeling,” Geogr. Anal., 1981.

Borovkova, Lopuha, and B. N. Ruchjana, “Generalized S-TAR with Random Weights,” in Proceeding of the 17th International Workshop on Statistical Modeling, 2002.

B. N. Ruchjana, “Study on the Weight Matrix in the Space-Time Autoregressive Model,” in Proceeding of the Tenth International Symposium on Applied Stochastic Models and Data Analysis (ASMDA), 2001, pp. 789–794.

B. N. Ruchjana, “Pemodelan Kurva Produksi Minyak Bumi Menggunakan Model Generalisasi STAR,” Bogor, 2001.

A. Iriany, Suhariningsih, B. N. Ruchjana, and Setiawan, “Prediction of Precipitation Data at Batu Town Using the GSTAR ( 1 , p ) -SUR Model,” J. Basic Appl. Sci. Res., vol. 3, no. 6, pp. 860–865, 2013.

A. D. Sulistyono, W. H. Nugroho, R. Fitriani, and A. Iriany, “Hybrid Model GSTAR-SUR-NN For Precipitation Data,” Cauchy, vol. 4, no. 2, p. 74, 2016.

A. D. Sulistyono, W. Hadi Nugroho, and A. Iriany, “Development of Hybrid Model GSTAR-SUR-NN and Aplication for Rainfall Forecasting,” in 1st International Conference Pure Applied Resources Univ. Muhammadiyah Malang, 2015, p. 104.

A. Iriany, W. M. Firdaus, W. H. Nugroho, and A. D. Sulistyono, “Rainfall Forecasting Using Gstar-Sur-Nn Approach in West Java Province,” in International Conference on Science, Engineering, Bulit Environment, and Social Science, 2016, p. 1.

Suhartono and R. M. Atok, “Pemilihan Bobot Lokasi yang Optimal pada Model GSTAR,” in Prosiding Konferensi Nasional Matematika XIII, 2006.

Suhartono and Subanar, “The Optimal Determination of Space Weight in GSTAR Model by using Cross-correlation Inference,” J. Quant. Methods, vol. 2, no. 2, pp. 45–53, 2006.

A. D. Sulistyono, W. H. Nugroho, and A. Iriany, “Location Weight of GSTAR Model for Heterogeneity Variance of Precipitation Data,” in International Conference on Science, Engineering, Bulit Environment, and Social Science, 2016, p. 6.

T. V. Apanasovich and M. G. Genton, “Cross-covariance functions for multivariate random fields based on latent dimensions,” Biometrika, vol. 97, no. 1, pp. 15–30, 2010.

S. Efromovich and E. Smirnova, “Statistical Analysis of Large Cross-Covariance and Cross-Correlation Matrices Produced by fMRI Images,” J. Biom. Biostat., vol. 05, no. 02, 2013.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.