Spatio-Temporal Model and Big Data Approach: GSTARIMA-ARCH Model for Rainfall Forecasting
Putri Monika (a*), Budi Nurani Ruchjana (b) , Atje Setiawan Abdullah (c) , Rahmat Budiarto (d)

(a) Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
*Correspondence: putri17001[at]mail.unpad.ac.id
(b) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran,
Sumedang 45363, Indonesia
(c) Department of Computer Science, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
(d) College of Computer Science and Information Technology, Al-Baha University, Alaqiq 65779-7738, Saudi Arabia

Abstract

Spatio-Temporal (ST) model is an advanced statistical model in stochastic modeling that is widely used for space-time data forecasting applications. This research integrates the ST model known as the Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) model with the Autoregressive Conditional Heteroskedasticity (ARCH) model. The GSTARIMA-ARCH model is part of complex statistical and mathematical analysis. This model has the ability to capture time and space patterns, and can handle non-constant (heteroscedastic) error variance in the data. The integration of the GSTARIMA-ARCH model in this study is used for rainfall forecasting with a big data approach. Rainfall observation data in this study is taken from NASA POWER (Prediction of Worldwide Energy Resources) which is big data and contains global climatology information. GSTARIMA-ARCH analysis and modeling requires a sophisticated data analytics life cycle methodology for more efficient data processing and more accurate forecasting. The analysis on real data in this study involves rainfall data from districts and cities in Java Island, Indonesia. Rainfall data was selected from 1982 to 2024 with a daily time span. The results of rainfall forecasting with the GSTARIMA-ARCH model provide accurate results shown by statistical evaluation of the calculation of the Mean Absolute Percentage Error (MAPE) value. The development of the GSTARIMA-ARCH model makes a significant contribution in the application of statistical and mathematical analysis, especially in the field of stochastic modeling. The results of rainfall forecasting can be utilized by agencies in the fields of meteorology, agriculture, and natural resource processing.

Keywords: GSTARIMA- ARCH- Stochastic Modeling- Big Data- Heteroskedastic- Rainfall

Topic: Probability and Stochastic Analysis