Integrating Time Series Models and Unsupervised Learning for Gold Price Forecasting

Gold has long been considered a reliable safe-haven asset, especially during times of financial turmoil. This paper uses an ARIMAX model with exogenous variables to forecast gold prices. Specifically, this essay uses technical indicators (log returns, volatility, and momentum) to identify market states and apply K-means clustering to classify these states. Then this paper generalizes the clustering results to unseen data using CART decision trees, thereby taking the market state forecast as an exogenous input. The final ARIMAX model is built using the auto.arima() function based on a stationary difference series, and the residual diagnostics validate the model. Empirical results show that most of the predicted prices are within the 95% confidence interval, and the introduction of the market state variable significantly improves the forecasting performance. The proposed method achieves a low MAPE of 1.25%, showing a high forecasting accuracy. This approach highlights the potential of combining unsupervised learning with time series models for more effective financial forecasting.