Comparing Areal and Grid Supports for Fire Radiative Power within a GSTAR (p; λ₁, λ₂, …, λₚ) Framework

Zuleha Zuleha; Nur'ainul Miftahul Huda; Nurfitri Imro'ah

doi:10.31764/jtam.v10i2.36663

Comparing Areal and Grid Supports for Fire Radiative Power within a GSTAR (p; λ₁, λ₂, …, λₚ) Framework

Zuleha Zuleha, Nur'ainul Miftahul Huda, Nurfitri Imro'ah

Abstract

Forest fire phenomena exhibit spatial interdependence and temporal dependence, necessitating a spatiotemporal modeling approach to capture the dynamics of fire occurrences. This study models and predicts forest fires using Fire Radiative Power (FRP) as an indicator of fire intensity. Weekly hotspot data from NASA FIRMS, covering the period from July 2024 to August 2025, were analyzed using the Generalized Space-Time Autoregressive (GSTAR) model. The modeling was conducted by considering various forms of spatial partitioning and spatial weight matrices to capture inter-location dependencies. Four spatial partitioning schemes were employed: areal, and grids of 0.50°×0.50°, 1.00°×1.00°, and 1.25°×1.25°; alongside three spatial weight matrices: Queen Contiguity, Rook Contiguity, and Inverse Distance Weighting (IDW). The temporal order and spatial lag were determined using STACF and STPACF plots. From these combinations, 42 GSTAR models were constructed and evaluated through a three-stage process of estimation and residual diagnostic testing. The results indicate that the GSTAR (1;1) model with a 1.00°×1.00° grid and Rook Contiguity and IDW spatial weight matrices is the best-performing model. This model satisfies the white noise assumption and yields a Root Mean Square Error (RMSE) of 6.866, which is the smallest among all evaluated models. The estimates indicate that fires at a given location are influenced by prior conditions and spatial interactions with surrounding areas, suggesting that the GSTAR model supports spatiotemporal monitoring and early warning systems.

Keywords

Spatial-Temporal; GSTAR; Grid; Weight Matrix; FRP.

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References

Abdullah, A. S., Matoha, S., Lubis, D. A., Falah, A. N., Jaya, I. G. N. M., Hermawan, E., & Ruchjana, B. N. (2018). Implementation of Generalized Space Time Autoregressive (GSTAR)-Kriging model for predicting rainfall data at unobserved locations in West Java. Applied Mathematics and Information Sciences, 12(3), 607–615. https://doi.org/10.18576/amis/120316

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

Ayyash, M. Y., Huda, N. M., & Imro’ah, N. (2025). The GSTAR (1;1) Modelling with Three Combination of the Grid Sizes and Spatial Weight Matrix in Forest Fires Cases. JTAM (Jurnal Teori Dan Aplikasi Matematika), 9(1), 134–146. https://doi.org/10.31764/jtam.v9i1.27543

Cahyono, S. A., P Warsito, S., Andayani, W., & H Darwanto, D. (2015). Faktor-Faktor Yang Mempengaruhi Kebakaran Hutan Di Indonesia Dan Implikasi Kebijakannya. Jurnal Sylva Lestari, 3(1), 103. https://doi.org/10.23960/jsl13103-112

Dare, J., Patrick, A. O., & Oyewola, D. O. (2022). Comparison of Stationarity on Ljung Box Test Statistics for Forecasting. Earthline Journal of Mathematical Sciences, 8(2), 325–336. https://doi.org/10.34198/ejms.8222.325336

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

Huda, N. M., & Imro’ah, N. (2023). Determination of the best weight matrix for the Generalized Space Time Autoregressive (GSTAR) model in the Covid-19 case on Java Island, Indonesia. Spatial Statistics, 54, 100734. https://doi.org/10.1016/j.spasta.2023.100734

Huda, N. M., & Imro’ah, N. (2024). Covid-19 case modeling in Java Island using a spatial model, GSTAR(1;1), with modified spatial weights: Queen contiguity weight matrix. AIP Conference Proceedings, 2891(1), 090009. https://doi.org/10.1063/5.0201676

Huda, N. M., Imro’ah, N., Arini, N. F., Utami, D. S., & Umairah, T. (2023). Looking at GDP from a Statistical Perspective: Spatio-Temporal GSTAR(1;1) Model. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(4), 976–988. https://doi.org/10.31764/jtam.v7i4.16236

Huda, N. M., Mukhaiyar, U., & Pasaribu, U. S. (2021). The approximation of GSTAR model for discrete cases through INAR model. Journal of Physics: Conference Series, 1722(1), 012100. https://doi.org/10.1088/1742-6596/1722/1/012100

Imro’ah, N., Huda, N. M., Pratiwi, H., & Ayyash, M. Y. (2025). A Hybrid ARIMA-Intervention Modelling for Forest Fire Risk in The Dry Season. CAUCHY: Jurnal Matematika Murni Dan Aplikasi, 10(2), 957–969. https://doi.org/10.18860/cauchy.v10i2.36741

Jalilov, S.-M., Rochmayanto, Y., Hidayat, D. C., Raharjo, J. T., Mendham, D., & Langston, J. D. (2025). Unveiling economic dimensions of peatland restoration in Indonesia: A systematic literature review. Ecosystem Services, 71, 101693. https://doi.org/10.1016/j.ecoser.2024.101693

Kusuma, V. M. A., Furqon, M. T., & Muflikhah, L. (2017). Implementasi metode fuzzy subtractive clustering untuk pengelompokan data potensi kebakaran hutan/lahan. Jurnal Pengembangan Teknologi Informasi Dan Ilmu Komputer, 1(9), 876–884. https://j-ptiik.ub.ac.id/index.php/j-ptiik/article/view/271

Mubarak, F., Aslanargun, A., & Sıklar, I. (2021). High Order Spatial Weighting Matrix Using Google Trends. International Journal of Research and Review, 8(11), 388–396. https://doi.org/10.52403/ijrr.20211150

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), 012003. https://doi.org/10.1088/1742-6596/2084/1/012003

Mukhaiyar, U., Mahdiyasa, A. W., Prastoro, T., Suherlan, B. C., Pasaribu, U. S., & Indratno, S. W. (2024). Spatial and Time Series Modelling for the Groundwater Level of Peatlands in Riau and Central Kalimantan, Indonesia. In W. F. Wan Yaacob, Y. B. Wah, & O. U. Mehmood (Eds.), Decision Mathematics, Statistical Learning and Data Mining (pp. 89–104). Springer Nature. https://doi.org/10.1007/978-981-97-3450-4_7

NASA-FIRMS. (2025, September 1). NASA-FIRMS. https://firms.modaps.eosdis.nasa.gov/map/

Notonegoro, Y., Andriyana, Y., & Ruchjana, B. (2024). Comparison of distance-based spatial weight matrix in modeling Internet signal strengths in Tasikmalaya regency using logistic spatial autoregressive model. International Journal of Data and Network Science, 8(2), 893–906. https://doi.org/10.5267/j.ijdns.2023.12.016

Nurhayati, N., Hamidi, M. R., Mukhaiyar, U., & Sari, K. N. (2025). Cross-Correlation Analysis in Evaluating Spatio-Temporal Data Dependence of Climate Variables Through the GSTAR Model. Jurnal Matematika, Statistika Dan Komputasi, 21(3), 813–831. https://doi.org/10.20956/j.v21i3.43665

Omar, M. S., Ifandi, E., Sukri, R. S., Kalaitzidis, S., Christanis, K., Lai, D. T. C., Bashir, S., & Tsikouras, B. (2022). Peatlands in Southeast Asia: A comprehensive geological review. Earth-Science Reviews, 232, 104149. https://doi.org/10.1016/j.earscirev.2022.104149

Pasaribu, U., Mukhaiyar, U., & Heriawan, M. (2018). Spatial weight determination of GSTAR (1; 1) model by using kernel function. Journal of Physics: Conference Series, 1028(1), 012223. https://doi.org/10.1088/1742-6596/1028/1/012223

Pasaribu, U. S., Mukhaiyar, U., Heriawan, M. N., & Yundari, Y. (2022). Generalized Space-Time Autoregressive Modeling of the Vertical Distribution of Copper and Gold Grades with a Porphyry-Deposit Case Study. International Journal on Advanced Science, Engineering and Information Technology, 12(5), 2030–2038. https://doi.org/10.18517/ijaseit.12.5.14835

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), e06025. https://doi.org/10.1016/j.heliyon.2021.e06025

Pratiwi, H., Imro’ah, N., & Huda, N. M. (2025). Forest Fire Analysis From Perspective Of Spatial-Temporal Using Gstar (p;λ_1,λ_2,…,λ_p) Model. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 19(2), Article 2. https://doi.org/10.30598/barekengvol19iss2pp1379-1392

Pratiwi, H., Imro’ah, N., Huda, N. M., & Ayyash, M. Y. (2025). Comparison Of Weight Matrix In Hotspot Modeling In West Kalimantan Using The Gstar Method. Jurnal Matematika UNAND, 14(1), 31–45. https://doi.org/10.25077/jmua.14.1.31-45.2025

Purwaningsih, T., Winarko, E., & Mustofa, K. (2025). Enhancing Accuracy of Spatiotemporal Model Estimation Using Modified Binary Distance Spatiotemporal Weight Matrix. International Journal of Intelligent Engineering & Systems, 18(8), 383–397. https://doi.org/10.22266/ijies2025.0930.24

Pusporani, E., Yuniar, M. A. D. P., Fajrina, S. A. N., Alexandra, V. A., & Mardianto, M. F. F. (2024). Generalized Space Time Autoregressive (GSTAR) Modeling in Predicting the Price of Bird’s Eye Chili in East Java, West Java, and Central Java. CAUCHY: Jurnal Matematika Murni Dan Aplikasi, 9(2), Article 2. https://doi.org/10.18860/ca.v9i2.25730

Ray, T., Malasiya, D., Verma, A., Purswani, E., Qureshi, A., Khan, M. L., & Verma, S. (2023). Characterization of spatial–temporal distribution of forest fire in Chhattisgarh, India, using MODIS-based active fire data. Sustainability, 15(9), 7046. https://doi.org/10.3390/su15097046

Roza, A., Violita, E. S., & Aktivani, S. (2022). Study of Inflation using Stationary Test with Augmented Dickey Fuller & Phillips-Peron Unit Root Test (Case in Bukittinggi City Inflation for 2014-2019). EKSAKTA: Berkala Ilmiah Bidang MIPA, 23(02), Article 02. https://doi.org/10.24036/eksakta/vol23-iss02/303

Setiawan, S., Wahyuningrum, S. R., & Akbar, M. S. (2016). GSTARX-GLS model for spatio-temporal data forecasting. Malaysian Journal of Mathematical Sciences, 10, 91–103. https://scholar.its.ac.id/en/publications/gstarx-gls-model-for-spatio-temporal-data-forecasting/

sipongi.menlhk.go.id. (2025, September 1). Sipongi.menlhk.go.id. https://sipongi.menlhk.go.id/

Umer, U. M., Sevil, T., & Sevil, G. (2018). Forecasting performance of smooth transition autoregressive (STAR) model on travel and leisure stock index. The Journal of Finance and Data Science, 4(2), 90–100. https://doi.org/10.1016/j.jfds.2017.11.006

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), Article 3. https://doi.org/10.20956/j.v20i3.34305

Yundari, Pasaribu, U. S., Mukhaiyar, U., & Heriawan, M. N. (2018). Spatial Weight Determination of GSTAR(1;1) Model by Using Kernel Function. Journal of Physics: Conference Series, 1028(1), 012223. https://doi.org/10.1088/1742-6596/1028/1/012223

Yundari, Y., Rahmawati, A., & Pratiwi, Y. E. (2025). GSTAR (1;1) Transfer Function Model for Forecasting Chili Prices with Rainfall Effect. ZERO: Jurnal Sains, Matematika Dan Terapan, 9(2), 511–523. https://doi.org/10.30829/zero.v9i2.26119

DOI: https://doi.org/10.31764/jtam.v10i2.36663