Stochastic modelling of the monthly average maximum and minimum temperature patterns in India 1981–2015

Abstract

The paper investigates the stochastic modelling and forecasting of monthly average maximum and minimum temperature patterns through suitable seasonal auto regressive integrated moving average (SARIMA) model for the period 1981–2015 in India. The variations and distributions of monthly maximum and minimum temperatures are analyzed through Box plots and cumulative distribution functions. The time series plot indicates that the maximum temperature series contain sharp peaks in almost all the years, while it is not true for the minimum temperature series, so both the series are modelled separately. The possible SARIMA model has been chosen based on observing autocorrelation function (ACF), partial autocorrelation function (PACF), and inverse autocorrelation function (IACF) of the logarithmic transformed temperature series. The SARIMA (1, 0, 0) × (0, 1, 1)12 model is selected for monthly average maximum and minimum temperature series based on minimum Bayesian information criteria. The model parameters are obtained using maximum-likelihood method with the help of standard error of residuals. The adequacy of the selected model is determined using correlation diagnostic checking through ACF, PACF, IACF, and p values of Ljung–Box test statistic of residuals and using normal diagnostic checking through the kernel and normal density curves of histogram and Q–Q plot. Finally, the forecasting of monthly maximum and minimum temperature patterns of India for the next 3 years has been noticed with the help of selected model.