Cross-Correlation Analysis in Evaluating Spatio-Temporal Data Dependence of Climate Variables  Through the GSTAR Model

Nurhayati Nurhayati; Muhammad Rozzaq Hamidi; Utriweni Mukhaiyar; Kurnia Novita Sari

doi:10.20956/j.v21i3.43665

Authors

Nurhayati Nurhayati Institut Teknologi Bandung, Indonesia
Muhammad Rozzaq Hamidi Institut Teknologi Bandung
Utriweni Mukhaiyar Institut Teknologi Bandung
Kurnia Novita Sari Institut Teknologi Bandung

DOI:

https://doi.org/10.20956/j.v21i3.43665

Keywords:

Climate variables, cross-correlation, dependence, estimation, space-time

Abstract

Climate change analysis requires an approach which is capable to accommodate the dynamics of relationships between climatological variables in space and time dimensions. Temperature, humidity, and rainfall vary temporally and exhibit spatial dependence across locations. This study applies the Generalized Space-Time Autoregressive (GSTAR) model to analyze the spatial and temporal dependence patterns of climate variables in Tasikmalaya. The novelty of this study lies in the cross-correlation analysis of climate variables using actual data and model estimation results. This analysis can be used to assess how well the GSTAR model maintains the spatio-temporal dependence pattern. GSTAR modeling is performed by applying the Three-Stage Iterative Box-Jenkins method to space-time data. The results indicate that GSTAR(3;1,1,1) is the best-fitting model. Furthermore, this model consistently captures historical data patterns and accommodates the dynamic dependencies between climate variables at the two observation locations. The results show that the GSTAR(3;1,1,1) model consistently represents historical data patterns and accommodates the dynamics of relationships between meteorological variables at the observed locations. This finding confirms that the GSTAR model is an effective approach for capturing the spatio-temporal dependence of climate data, particularly in preserving the natural relationship patterns in actual data.

References

[1] Aprianti, A., Faulina, N., & Usman, M., 2024. Generalized Space Time Autoregressive (GSTAR) Model for Air Temperature Forecasting in the South Sumatera, Riau, and Jambi Provinces. InPrime: Indonesian Journal of Pure and Applied Mathematics, 6(1), 1–13. https://doi.org/10.15408/inprime.v6i1.36049

[2] Arini, N. F., Huda, N. M., & Andani, W., 2023. Perbandingan Matriks Bobot Invers Jarak dan Bobot Seragam pada Model (1;1) untuk Data Indeks Harga Konsumen (Studi Kasus: Indeks Harga Konsumen di Kalimantan Barat). Tensor: Pure and Applied Mathematics Journal, 4(1), 27–36. https://doi.org/10.30598/tensorvol4iss1pp27-36

[3] Borovkova, S., Lopuhaä, H. P., & Ruchjana, B. N., 2008. Consistency and asymptotic normality of least squares estimators in generalized STAR models. Statistica Neerlandica, 62(4), 482–508. https://doi.org/10.1111/j.1467-9574.2008.00391.x

[4] Hadi, A. F., Yudistira, I., Anggraeni, D., & Hasan, M., 2018. The Geographical Clustering of the Rainfall Stations on Seasonal GSTAR Modeling for Rainfall Forecasting. Journal of Physics: Conference Series, 1028(1), 1–12. https://doi.org/10.1088/1742-6596/1028/1/012238

[5] Harini, S., & Nuronia, N., 2020. Determination of consumer price index with generalized space-time autoregressive. IOP Conference Series: Earth and Environmental Science, 456(1). https://doi.org/10.1088/1755-1315/456/1/012076

[6] Hestuningtias, F., & Kurniawan, M. H. S., 2023. The Implementation of the Generalized Space-Time Autoregressive (GSTAR) Model for Inflation Prediction. Enthusiastic : International Journal of Applied Statistics and Data Science, 3(2), 176–188. https://doi.org/10.20885/enthusiastic.vol3.iss2.art5

[7] Mahmoudi, M. R., & Zarei, A. R., 2023. Modified version of the cross-correlation function to measure drought occurrence time-delay correlation. Journal of Water and Climate Change, 14(2), 454-476.

[8] Koskinas, A., Zaharopoulou, E., Pouliasis, G., Deligiannis, I., Dimitriadis, P., Iliopoulou, T., & Koutsoyiannis, D., 2022. Estima,ting the Statistical Significance of Cross–Correlations between Hydroclimatic Processes in the Presence of Long–Range Dependence. Earth, 3(3), 1027-1041.

[9] Mohamed, N., M., Rahman, N. H., & Zulkafli, H. S., 2023. Generalized Space-Time Autoregressive (GSTAR) for Forecasting Air Pollutant Index in Selangor. Journal of Quality Measurement and Analysis JQMA, 19(3), 143-153

[10] Monika, P., Ruchjana, B. N., & Abdullah, A. S., 2022. GSTARI-X-ARCH Model with Data Mining Approach for Forecasting Climate in West Java. Computation, 10(12), 204. https://doi.org/10.3390/computation10120204

[11] Mukhaiyar, U., Bilad, B. I., & Pasaribu, U. S., 2021. The generalized STAR modelling with minimum spanning tree approach of weight matrix for COVID-19 case in Java Island. Journal of Physics: Conference Series, 2084(1). https://doi.org/10.1088/1742-6596/2084/1/012003

[12] Mukhaiyar, U., Huda, N. M., Sari, K. N., & Pasaribu, U. S., 2020. Analysis of generalized space time autoregressive with exogenous variable (GSTARX) model with outlier factor. In Journal of Physics: Conference Series (Vol. 1496, No. 1, p. 012004). IOP Publishing.

[13] Mukhaiyar, U., Mahdiyasa, A. W., Sari, K. N., & Noviana, N. T., 2024. The generalized STAR modeling with minimum spanning tree approach of spatial weight matrix. Frontiers in Applied Mathematics and Statistics, 10, 1417037.

[14] Mukhaiyar, U., & Pasaribu, U. S., 2012. A new procedure for generalized STAR modeling using IAcM approach. ITB Journal of Science, 44 A(2), 179–192. https://doi.org/10.5614/itbj.sci.2012.44.2.7

[15] Mukhaiyar, U., & Ramadhani, S., 2022. The Generalized STAR Modeling with Heteroscedastic Effects. CAUCHY: Jurnal Matematika Murni Dan Aplikasi, 7(2), 158–172. https://doi.org/10.18860/ca.v7i2.13097

[16] Nishioka, M., 2024. Cross-Correlation between Global Temperature and Atmospheric CO2 with a Temperature-Leading Time Lag. Atmospheric and Climate Sciences, 14(4), 484-494.

[17] Palmeira, A., Pereira, É., Ferreira, P., Diele-Viegas, L. M., & Moreira, D. M., 2022. Long-term correlations and cross-correlations in meteorological variables and air pollution in a coastal urban region. Sustainability, 14(21), 14470.

[18] Pasaribu, U. S., Mukhaiyar, U., Huda, N. M., Sari, K. N., & Indratno, S. W., 2021. Modelling COVID-19 growth cases of provinces in java Island by modified spatial weight matrix GSTAR through railroad passenger’s mobility. Heliyon, 7(2). https://doi.org/10.1016/j.heliyon.2021.e06025

[19] Rahmani, U. P., 2025. Penerapan Model Generalized Space Time Autoregressive (GSTAR) Pada Data Inflasi Beberapa Kota. Sciencestatistics: Journal of Statistics, Probability, and Its Application, 3(1), 38–54

[20] Sulistyono, A. D., Hartawati, H., Suryawardhani, N. W., Iriany, A., & Iriany, A., 2020. Cross-Covariance Weight of GSTAR-SUR Model for Rainfall Forecasting in Agricultural Areas. CAUCHY: Jurnal Matematika Murni dan Aplikasi, 6(2), 49-57.

[21] Utami, R., Mukhaiyar, U., Mardiyah, N., Sa’adah, Y., & Widyawati, E., 2024. Spatial Weighting Selection in GSTAR and S-GSTAR Models for Temperature Prediction. Jurnal Matematika, Statistika Dan Komputasi, 20(3), 639–653. https://doi.org/10.20956/j.v20i3.34305

[22] Yundari, Y., Huda, N. M., Pasaribu, U., & Mukhaiyar, U., 2020. Stationary Process in GSTAR(1;1) through Kernel Function Approach. AIP Conference Proceedings, 2268(1).

[22] Zaki, A., Irwan, & Lutfiah, 2025. Application of the Generalized Space Time Autoregressive (Gstar) Method in Forecasting the Consumer Price Index in Five Cities of South Sulawesi Province. Barekeng, 19(1), 375–384. https://doi.org/10.30598/barekengvol19iss1pp375-384.