Comparison of Models (SARIMA, ARFIMA, AND SARFIMA) in the Presence of Long Memory

One of the greatest challenges faced in data analysis is fitting the most appropriate model to a dataset. In reality, misspecification of the model has resulted in several wrong decisions in data science. This work compares the efficiency of modelling a time series with seasonal long memory properties with SARIMA, ARFIMA and SARFIMA models. Monthly average global temperature data was used for the this illustration. The temperature data displayed signs of long memory as the ACF plot decayed slowly on further scrutiny, the Hurst exponent produced by R/S analysis we confirmed the presence of long memory.The ACF exhibited exponential decay and a sinusoidal pattern, suggesting non-stationarity and seasonality. Test for stationarity and seasonality were done to confirm these assertions from the plot. Finally, the AIC and BIC were used to evaluate the efficiency of all three models and the result shows that, in the presence of seasonality and long memory, the SARFIMA model was more efficient.