Trend analysis and SARIMA forecasting of mean maximum and mean minimum monthly temperature for the state of Kerala, India

Abstract

The development of temperature forecasting models for the state of Kerala using Seasonal Autoregressive Integrated Moving Average (SARIMA) method is presented in this article. Mean maximum and mean minimum monthly temperature data, for a period of 47 years, from seven stations, are studied and applied to develop the model. It is expected that the time-series datasets of temperature to display seasonality (and hence non-stationary), and a possible trend (due to the fact that the data spans 5 decades). Hence, the key step in the development of the models is the determination of the non-stationarity of the temperature time-series, and the transformation of the non-stationary time-series into a stationary time-series. This is carried out using the Seasonal and Trend decomposition using Loess technique and Kwiatkowski–Phillips–Schmidt–Shin test. Before carrying out this process, several preliminary tests are conducted for (1) finding and filling the missing values, (2) studying the characteristics of the data, and (3) investigating the presence of the trend and seasonality. The non-stationary temperature time-series are transformed to stationary temperature time-series, by one seasonal differencing and one first-order differencing. This information, along with the original time-series, is further utilized to develop the models using the SARIMA method. The parsimonious and best-fit SARIMA models are developed for each of the fourteen variables. The study revealed that $\text{SARIMA}(2,1,1)(1,1,1)_{12}$ as the ideal forecasting model for eight out of the fourteen time-series datasets.