A Hybrid Space–Time Modelling Approach for Forecasting Monthly Temperature

Spatio-temporal forecasting has various applications in climate, transportation, geo-statistics, sociology, economics and in many other fields of study. The modelling of temperature and its forecasting is a challenging task due to spatial dependency of time series data and nonlinear in nature. To address these challenges, in this study we proposed hybrid Space–Time Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroscedasticity (STARMA-GARCH) model in order to describe and identify the behaviour of monthly maximum temperature and temperature range in Bihar. At the modelling process of STARMA, spatial characteristics are incorporated into the model using a weight matrix based on great circle distance between the regions. The residuals from the fitted STARMA model have been tested for checking the behaviour of nonlinearity. Autoregressive Conditional Heteroscedasticity-Lagrange Multiplier (ARCH-LM) test has been carried out for the ARCH effect. The test results revealed that presence of both nonlinearity and ARCH effect. Hence, GARCH modelling is necessary. Therefore, the hybrid STARMA-GARCH model is used to capture the dynamics of monthly maximum temperature and temperature range. The results of the proposed hybrid STARMA11,0,0-GARCH0,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{STARMA} \left({1}_{1}, 0, 0\right)-\mathrm{GARCH} \left(0, 1\right)$$\end{document} model have better modelling efficiency and forecasting precision over STARMA11,0,0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{STARMA }\left({1}_{1}, 0, 0\right)$$\end{document} model.