Assess the performance of the ARIMA and ARIMAX models to forecast time series data.

Abstract

This study evaluates the forecasting performance of time series models for predicting the price of 18-carat broken gold in the parallel market of Tripoli, Libya. While the ARIMA model is widely used for univariate time series forecasting, it often fails to account for external factors. In contrast, the ARIMAX model incorporates exogenous variables, potentially improving accuracy. This research compares four models: ARIMA, ARIMAX, a simple linear regression model, and a mixed model (combining ARIMA with residuals from an external variable model). The dataset spans from February 8, 2019, to April 30, 2019, with the dollar price as the exogenous variable.   The results indicate that the ARIMAX(1,2,0)(1,1,0) model outperforms the others, demonstrating superior forecasting accuracy. The mixed model (ARIMA + residuals) ranks second, followed by the ARIMA(1,2,0) model, while the simple linear regression performs the worst. These findings are validated using RMSE and R² metrics. The study concludes that incorporating external variables, as in ARIMAX, significantly enhances gold price forecasting, making it a preferred approach over traditional univariate models.