Hybrid LSTM–XGBoost Model with Residual Error Correction for Multivariate Gold Price Forecasting Using Macroeconomic Indicators

Gold plays a critical role in financial markets and is widely regarded as a hedge and safe-haven asset during periods of economic uncertainty. Accurate gold price forecasting is therefore essential for investment strategy, portfolio allocation, and risk management. This study proposes a hybrid forecasting framework that integrates Long Short-Term Memory (LSTM) and Extreme Gradient Boosting (XGBoost) through explicit residual error correction for multivariate gold price prediction. Monthly gold prices and selected macroeconomic indicators, including CPI, DXY, US10Y, WTI, and SP 500, covering the period from 2010 to 2025, are employed. The dataset consists of 192 monthly observations. Prior to modeling, logarithmic transformation, stationarity testing using the Augmented Dickey–Fuller (ADF) test, first-order differencing, and Min–Max normalization are applied to ensure statistical validity and numerical stability. The LSTM component captures temporal dependencies in sequential data, while the XGBoost model nonlinearly models residual structures to enhance predictive performance. A 12-month sliding-window mechanism is employed to capture annual temporal dependencies, and the XGBoost component is trained to learn residual errors not explained by the LSTM forecasts. Empirical results demonstrate that the proposed hybrid model achieves superior accuracy compared to standalone LSTM, XGBoost, and ARIMA baselines, obtaining an RMSE of 0.0989, an MAE of 0.0691, and a MAPE of 0.8503 in the testing period. Diebold–Mariano tests confirm that the hybrid model significantly outperforms both LSTM and ARIMA (p 0.01). Walk-forward validation further indicates stable forecasting performance across rolling evaluation windows. The validation results demonstrate consistent predictive accuracy across multiple rolling windows, supporting the robustness and generalizability of the proposed framework. These findings suggest that integrating temporal learning with structured residual correction provides a robust, statistically grounded approach to multivariate gold price forecasting. Keywords: Gold price forecasting, Hybrid LSTM–XGBoost, Multivariate forecasting, Residual learning, Time series forecasting, Walk-forward validation.