Forecasting China's precious metal futures volatility: GBRT models and time-model dimension combination of Tree SHAP

This study introduces a diverse set of feature variables to evaluate the performance of various machine learning models in forecasting Realized Volatility (RV) of Shanghai gold and silver futures using a one-step-forward rolling algorithm. The findings reveal that Gradient Boosting Regression Trees (GBRT) outperform other models in forecasting within the precious metal futures market. We employ the discounted mean squared prediction error (DMSPE) method to combine three GBRT models, thereby enhancing the performance and robustness of the predictive models. The DMSPE-GBRT model consistently ranks second in predictive performance across both precious metal markets. Subsequently, this study combines the Tree SHapley Additive ExPlanation (SHAP) values of the DMSPE-GBRT model across both temporal and model dimensions, employing summary plots, heatmaps, and force plots to analyze the global and local interpretability of the time series predictions. The research uncovers local similarities in the contribution of feature variables within the same time frame, with the implied volatility indices of gold, as well as the London gold or silver, identified as significant factors influencing volatility forecasts. The variation in feature variable contributions during high-volatility periods across different markets can explain the characteristics of volatility changes. These findings provide comprehensive empirical evidence for the relationship among feature variables, Tree SHAP values and the prediction of precious metal futures volatility.