Short and Long Memory Models in Modeling Libyan GDP: An Applied Study using ARIMA and ARFIMA

Abstract

This paper aims to evaluate the ability of time series models in modeling Libyan GDP during the period 1960–2024. The analysis focuses on examining long memory properties and comparing the performance of the Autoregressive Integrated Moving Average (ARIMA) model with the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model. The results showed a general trend and long memory in the series with a fractional difference coefficient d = 0.495795. Unit root tests confirmed the non-stationarity of the original series versus the stationarity of the (fractional/first) difference series. Based on information criteria and forecast measures (AIC, SIC, and RMSE), the ARFIMA (0,0.495795,0) model outperforms traditional ARIMA models in characterizing the dynamics of Libyan GDP. These results provide a practical framework for improving the modeling of economic indicators and formulating economic policies in Libya.