Time Series Analysis Of Monthly Average Global Temperature: A Comparison Of Models (Sarima, Arfima And Sarfima):- Aruah Kelechi E

ABSTRACT One of the greatest challenges faced in data analysis is fitting the most appropriate model to a dataset. In reality, mis-specification of model has resulted in several wrong decisions in data science. This work compares three models to find the most suitable model for a time series with seasonal long memory properties with SARIMA, ARFIMA and SARFIMA models. Global average temperature data was used for the purpose of this illustration. The temperature data displayed signs oflong memory as the ACF plot decayed very slowly. On further scrutiny, using the Hurst exponent produced by Rescaled analysis (R/S), we confirmed the presence of long memory in the series. The ACF also displayed an exponential decay and a repeated sine movement indicating that the model is not stationary in trend and may be seasonal. Test for stationarity and seasonality were done to confirm these assertions from the plot. Finally, the AIC and BIC was used to evaluate the efficiency of all three models and the result shows that, in the presence ofseasonality and long memory, the SARFIMA model was more suitable.