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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Muhammad Rozzaq Hamidi
Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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SPATIO-TEMPORAL MODELING OF SEMI-HETEROSKEDASTIC RAINFALL DATA USING A GSTAR-GARCH FRAMEWORK Nurhayati Nurhayati; Muhammad Rozzaq Hamidi; Utriweni Mukhaiyar; Kurnia Novita Sari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3371-3390

Abstract

Rainfall often varies across time and space, with sudden and irregular changes that are difficult to capture. These variations are commonly linked to residual heteroskedasticity and spatial dependence, both of which can reduce the accuracy of statistical modeling when ignored. This study considers a semi-heteroskedastic setting, where residuals at one location remain stable while those at another show varying variance. To accommodate this mixed structure, we construct a covariance matrix that reflects both conditions. A hybrid model is then proposed by combining the Generalized Space-Time Autoregressive (GSTAR) framework with the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process. The GARCH component is used because it generalizes ARCH through a more flexible lag structure, allowing for better representation of volatility persistence and long-term fluctuations. The approach is applied to monthly average rainfall data retrieved from the NASA POWER database for two sites in Tasikmalaya Regency, Indonesia, which differ in distributional patterns and variability. The results show that the GSTAR-GARCH model can effectively capture spatial and temporal dependencies as well as volatility dynamics, performing consistently in both estimation and validation stages.
Co-Authors Kurnia Novita Sari Nurhayati Nurhayati Utriweni Mukhaiyar