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Journal : Science and Technology Indonesia

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Block Bootstrap for Spatiotemporal Data in Generalized Space Time Autoregressive (GSTAR) Sumarminingsih, Eni; Fitriani, Rahma; Darmanto; Maulana, Eka Dani; Aulia, Natasha; Ruszardi, Luzar Dwain
Science and Technology Indonesia Vol. 11 No. 2 (2026): April
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.2.701-731

Abstract

Generalized Space-Time Autoregressive is a model that can be used for data with spatial and temporal dependence. The GSTAR model is widely used in various phenomena such as rainfall, temperature, inflation, and others. GSTAR assumes normality of errors and non-autocorrelation. If the assumption of normality of errors is not met, then inference on parameters cannot be made. One solution to this problem is to use bootstrapping. However, bootstrapping for spatiotemporal data in the GSTAR model has not been developed. Therefore, this study aims to develop a bootstrapping method for spatiotemporal data in the GSTAR model. This development is done by adapting bootstrapping methods for time series data, namely, the non-overlapping block bootstrap (NBB) and the moving block bootstrap (MBB). This research continued with a series of simulations to evaluate the performance of the block bootstrap method as the number of observations, block length, and number of bootstrap replications were varied. Furthermore, the method’s effectiveness was tested using rainfall data from Malang Regency. Simulation results show that both resampling schemes satisfy the asymptotic condition, where the bias decreases monotonically with increasing sample size (T) and block length. MBB consistently produces lower bias than NBB due to its more intensive use of overlapping data, which effectively reduces boundary effects. Although inference on autoregressive parameters can be accurate, inference on spatial autoregressive parameters yields less satisfactory results, indicating the limitations of time blocks in capturing complex spatial dependencies. Increasing the number of replications above B=100 does not significantly improve the precision of the variance estimate, indicating computational efficiency at that threshold. The t-test results confirm that there is no statistically significant difference in performance between NBB and MBB. Nevertheless, MBB is more recommended for practical applications due to its higher information density and better estimation stability.
Co-Authors Abdullah Zailani Abu Mansur, Abu Agus Prayitno AGUS PRAYITNO Ahmad Zuhri Rosyidi Amalia, Amah Annisa Astrid Anwar, Muchammad Syaiful Aos Kuswandi Aprianingsih, Heny Ari Warokka, Ari Arvin Efriani Asy'arie, Bima Fandi Atanasius Priharyoto Bayuseno Aulia, Natasha Azizah, Suti Mega Nur Baehaqi Basuki Sri Rahayu BUDIYONO Budiyono Budiyono Cahyanto, Gilang eko Cholis, Muhammad Cukup Islamiarso Dhaniswara, Erwin Eni Sumarminingsih Eprianto Ernawati Budi Astuti Esti Setiawati Etheldreda Prabandasari Bria Fitri Oviyanti Fujiannor Rahman Gunarto, Julian Christhoper Hafel, Muhlis hidayat, dwi taufik Hizkia, Daud I Nyoman Jujur Imam Asrori Indah Hartati Irja Putra Pratama Josefphine, Christina Azazya Judijanto, Loso Karlina Hogiana Suprihadi Putri Kasinyo Harto Khoirul Anwar Kiring Yopi Kusala, Vajra Vidya Laeli Kurniasari Lalong, Etha Margharetha Linda Dwi Astuti Lisman Manurung LMS Kristiyanti, LMS LMS. Kristiyanti Loris M. Yogi Riyantama Isjoni Maryamah Maulana, Eka Dani Mauludin, Mochamad Subchan Ma’ruf, Muhammad Hasan Meli, Meli Puspita Muhammad Sirozi Muhammad, Adamu Abubakar Ningsi, Fitri Novriansyah, Robin Nunuk Herawati Nurhidayati Nuringsih Sujati Oktavianus Satu Pardana Wati, Sri Laksmi Paulus Wisnu Anggoro Prawibowo, Hartanto Putri, Netty Fitriana Qiftiyah, Maemunatussa’dayatul Rahma Fitriani Redata, Lira Renitasari, Delta Ayu Reynold, O. T Rifky Ismail Ruszardi, Luzar Dwain Saifullah, Aeb Sait abdullah Salindri Selly Susanti, Septiani Sepiana, Yelna Septiani, Reni Setyadi, Achmad Umar Sidi, Pramono Siti Fatimah Slamet Riadi Sri Laksmi Pardanawati, Sri Laksmi Sri Wardaya Suparlan . Suprihati Suprihati - Syahla Tabah Priangkoso Trisno, Indra Budi Tyas, Nofi Wahyuning Utami, Fuji Widianto Yonatan, Widianto Wikan Budi Utami Yelna Septiana Yenni Maria Sridarta Yulia Wahyuni Yulius Hari Yuris Setyoadi Zaneta, Aulia Zubairi, Ahmad