Gold Price Forecast for the Period 2010–2025 Using the ARIMAX–NGARCH Model

Abstract

Gold prices are influenced by various macroeconomic factors, particularly inflation and the USD/IDR exchange rate, and often exhibit fluctuating movements and volatile behavior over time. These characteristics require forecasting methods that can model both the mean structure and volatility dynamics of the data. This study aims to forecast the monthly price of the 1-gram EmasKITA product of PT Hartadinata Abadi Tbk using the ARIMAX–NGARCH model with inflation and the USD/IDR exchange rate as exogenous variables. The research employed monthly time-series data from January 2010 to December 2025. The analytical procedure included descriptive statistical analysis, stationarity testing using the Augmented Dickey–Fuller (ADF) test, ARIMAX modeling to capture the effects of macroeconomic variables on gold prices, and NGARCH modeling to account for heteroscedastic and asymmetric volatility. Model selection was based on the Akaike Information Criterion (AIC) and parameter significance tests. Forecasting performance was evaluated on the testing dataset using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The results show that the ARIMAX (1,0,0)–NGARCH (1,1) model is the best-performing model, yielding an RMSE of 338,994.81 and a MAPE of 12.51%. Forecasts for the January–May 2026 period indicate a gradual increase in gold prices of approximately 3.71%. These findings suggest that the ARIMAX–NGARCH model is capable of capturing both the influence of macroeconomic factors and the asymmetric volatility characteristics of PT Hartadinata Abadi Tbk’s gold prices, with moderate forecasting performance.