Modelling and Forecasting of Monthly Rainfall and Temperature Time Series Using SARIMA for Trend Detection- A Case Study of Umiam, Meghalaya (India)

Abstract

Seasonal Auto Regressive Integrative Moving Average Models (SARIMA) were developed for monthly rainfall, mean monthly maximum and minimum temperature time series for Umiam (Barapani), Meghalaya (India). The best model was selected based on the minimum values of AIC and BIC criteria as well as based on observing the ACF and PACF plot of residuals. SARIMA (5,1,2) x (1,1,1)12, SARIMA (2,1,2) x (2,1,1)12, SARIMA (6,1,4) x (2,1,3)12 models were found to be the best fit model for the monthly rainfall, mean monthly maximum  and minimum temperatures time series respectively. The adequacy of the SARIMA models was also verified using the Ljung-Box (Q) statistic test. McLeod-Li test and Engle’s ARCH LM test were carried out for residuals. The results indicated that there was no Arch effect in the established SARIMA models and models can be used for forecasting the future values for the year 2013 to 2028. The determination of trend in monthly rainfall, mean maximum and minimum temperatures in the forecasted series were done using different trend analysis techniques. For monthly rainfall and mean monthly minimum temperature time series, all the selected methods supported no significant trend. However, in the case of mean monthly maximum temperature time series, three selected methods supported falling trend.