Abstract
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 it 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 Heteroscadicity (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 by Brock, Dechert, and Scheinkman (BDS) and Autoregressive Conditional Heteroscadicity-Lagrange Multiplier (ARCH-LM) test for the behaviour of nonlinearity and ARCH effect respectively. 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 STARMA (1 1 , 0, 0)−GARCH (0, 1) model has better modelling efficiency and forecasting precision over STARMA (1 1 ,0, 0) model.