Time Series Analysis of Rainfall Using Seasonal ARIMA (SARIMA) and Sama Circular Model (SCM): Study from Vadamaradchi, Jaffna, Sri Lanka

Abstract

The time series analysis was performed with Seasonal Autoregressive Integrated Moving Average (SARIMA) and Sama circular model (SCM) for the rainfall of Ampan, Karaveddi, and Puloly regions of Jaffna to understand the behaviour of rainfall and forecast it with a suitable model. Minitab 17 software was used to run the model with the available monthly data from 2013 to 2019. Time series plots were used for pattern recognition, the independence of the residuals was checked using autocorrelation function (ACF), and Lijung-Box Q statistics (LBQ). The normality of residuals was checked using probability plot. The model with the lowest predicting errors was selected to forecast the future values. The monthly rainfall fluctuates around the mean of 41.6, 71.9, and 35.3 mm for Ampan, Karaveddi, and Puloly respectively. The models SARIMA (0,0,0) (0,1,1)6, SARIMA (1,2,1) (0,1,1)6, and SARIMA (1,1,0) (0,1,1)6 were found as most appropriate for Ampan, Karaveddi, and Puloly respectively and 𝑌𝑡 = 𝑌𝑡−1 − 0.18 + 23.5 sin 2𝜔𝑡 + 28.5 cos 1.5𝜔𝑡 + 20.10 cos 2𝜔𝑡 − 26.47 cos 5.5𝜔𝑡 , 𝑌𝑡 = 𝑌𝑡−1 −2𝑌𝑡−2 −5.9+ 73.5 sin 4.5𝜔𝑡 and 𝑌𝑡 = 𝑌𝑡−1 − 2𝑌𝑡−2 + 0.69 + 23.17 cos 5.5𝜔𝑡 were found as most appropriate SCM for Ampan, Karaveddi, and Puloly respectively. Among these models, SCM predicts reliable data with minimum error and it finds the seasonal and cyclic pattern of the rainfall. A five-month seasonal pattern and cyclic behaviour at 13 - months interval was noted in Ampan. Similarly, 10 - months seasonal pattern was observed in Karaveddi. The Puloly region expressed the cyclic pattern of rainfall only at 13-month interval. AD value is 0.40, 0.63 and 0.68 for Ampan, Karaveddi and Puloly respectively. The decreasing trend of estimated rainfall in Ampan (0.21 mm/year) and increasing trend in Puloly (1.15 mm/year) and Karaveddi (0.61 mm/year) is an alarming sign to the agriculture sector.