SARIMA modeling of the monthly average maximum and minimum temperatures in the eastern plateau region of India

Abstract

The SARIMA time series model is fitted to the monthly average maximum and minimum temperature data sets collected at Giridih, India for the years 1990-2011. From the time-series  plots, we observe that the patterns of both the series are quite different; maximum temperature series contain sharp peaks in almost all the years while it is not true for the minimum temperature series and hence both the series are modeled separately (also for the sake of simplicity). SARIMA models are selected based on observing autocorrelation function (ACF) and partial autocorrelation function (PACF) of the monthly temperature series. The model parameters are obtained by using maximum likelihood method with the help of three tests [i.e., standard error, ACF and PACF of residuals and Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and corrected Akaike Information Criteria (AICc)]. Adequacy of the selected models is determined using diagnostic checking with the standardized residuals, ACF of residuals, normal Q-Q plot of the standardized residuals and p-values of the Ljung-Box statistic. The models ARIMA (1; 0; 2) × (0; 1; 1)₁₂  and ARIMA (0; 1; 1) × (1; 1; 1)₁₂  are finally selected for forecasting of monthly average maximum and minimum temperature values respectively for the eastern plateau region of India.