SPATIO-TEMPORAL MODELING OF SEMI-HETEROSKEDASTIC RAINFALL DATA USING A GSTAR-GARCH FRAMEWORK

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.