ISSN: 2225-8329
Open access
This study develops a leakage-free, regime-conditioned framework for forecasting silver futures returns and evaluating risk-aware performance under volatility shock regimes. Using daily SI=F data from January 2010 to January 2026, we construct log returns and a realized-volatility proxy RV20, and identify shock regimes via a rolling quantile threshold estimated strictly from past information, ensuring that regime classification remains executable out of sample. We benchmark a random-walk return forecast against a regularized linear ARX model and gradient-boosted trees and implement an ablation design to isolate the incremental contribution of monthly macro variables (oil, gold, and World Bank silver prices) that are aligned to daily observations using a one-month lag to prevent look-ahead bias. All models are evaluated through a rolling out-of-sample protocol with a frozen-hyperparameter strategy to preclude implicit test-time optimization. Results show that strong baselines remain difficult to outperform in RMSE, particularly during shock regimes, while directional accuracy exhibits horizon dependence, with linear dynamics more informative at short horizons and non-linear learners comparatively more stable at longer horizons. Predictive-accuracy tests indicate that macro augmentation does not deliver robust gains relative to strong benchmarks once information timing and estimation risk are controlled. To quantify uncertainty, we construct online rolling conformal prediction intervals and report regime-conditional calibration. Intervals widen materially during shocks, yet coverage deteriorates in stress states, consistent with distribution shift, implying that calibration behavior itself can serve as an operational trigger for hedging adjustment or capital preservation. Overall, the evidence emphasizes fair comparisons under identical information sets and highlights uncertainty quantification as a decision-critical output when return predictability is intrinsically limited.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71(2), 579–625. https://doi.org/10.1111/1468-0262.00418
Angelopoulos, A. N., & Bates, S. (2021). A gentle introduction to conformal prediction and distribution-free uncertainty quantification. arXiv. https://arxiv.org/abs/2107.07511
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1
Chen, T., & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 785–794). ACM. https://doi.org/10.1145/2939672.2939785
Croushore, D. (2006). Forecasting with real-time macroeconomic data. In G. Elliott, C. W. J. Granger, & A. Timmermann (Eds.), Handbook of Economic Forecasting (Vol. 1, pp. 961–982). Elsevier. https://doi.org/10.1016/S1574-0706(05)01017-3
Diebold, F. X. (2015). Comparing predictive accuracy, twenty years later: A personal perspective on the use and abuse of Diebold–Mariano tests. Journal of Business & Economic Statistics, 33(1), 1–9. https://doi.org/10.1080/07350015.2014.983236
Diebold, F. X., & Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263. https://doi.org/10.1080/07350015.1995.10524599
Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. https://doi.org/10.2307/1912773
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417. https://doi.org/10.1111/j.1540-6261.1970.tb00518.x
Foroni, C., Marcellino, M., & Schumacher, C. (2015). Unrestricted mixed data sampling (U-MIDAS): MIDAS regressions with unrestricted lag polynomials. Journal of Applied Econometrics, 30(3), 495–512. https://doi.org/10.1002/jae.2369
Ghysels, E., Santa-Clara, P., & Valkanov, R. (2006). Predicting volatility: Getting the most out of return data sampled at different frequencies. Journal of Econometrics, 131(1–2), 59–95. https://doi.org/10.1016/j.jeconom.2005.01.004
Gibbs, I., & Candès, E. J. (2021). Adaptive conformal inference under distribution shift. Advances in Neural Information Processing Systems. https://arxiv.org/abs/2106.00170
Giacomini, R., & White, H. (2006). Tests of conditional predictive ability. Econometrica, 74(6), 1545–1578. https://doi.org/10.1111/j.1468-0262.2006.00718.x
Hamilton, J. D., & Susmel, R. (1994). Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics, 64(1–2), 307–333. https://doi.org/10.1016/0304-4076(94)90067-1
Jabeur, S. B., Mefteh-Wali, S., & Viviani, J.-L. (2024). Forecasting gold price with the XGBoost algorithm and SHAP interaction values. Annals of Operations Research, 334(1–3), 679–699. https://doi.org/10.1007/s10479-021-04187-w
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018). Distribution-free predictive inference for regression. Journal of the American Statistical Association, 113(523), 1094–1111. https://doi.org/10.1080/01621459.2017.1307116
Luna, M., Perez-Mon, O., & Becker, J. L. (2025). Forecasting and managing price volatility in salmon production: A hybrid system using conformal prediction and dynamic hedging. International Journal of Production Economics. https://doi.org/10.1016/j.ijpe.2025.109726
Naeem, M., Tiwari, A. K., Mubashra, S., & Shahbaz, M. (2019). Modeling volatility of precious metals markets by using regime-switching GARCH models. Resources Policy, 64, 101497. https://doi.org/10.1016/j.resourpol.2019.101497
Stark, T., & Croushore, D. (2002). Forecasting with a real-time data set for macroeconomists. Journal of Macroeconomics, 24(4), 507–531. https://doi.org/10.1016/S0164-0704(02)00062-9
Vovk, V., Gammerman, A., & Shafer, G. (2005). Algorithmic learning in a random world. Springer. https://doi.org/10.1007/b106715
Wang, S., & Zhang, T. (2024). Predictability of commodity futures returns with machine learning models. Journal of Futures Markets, 44(2), 302–322. https://doi.org/10.1002/fut.22471
Wang, X., Wu, J., & Liu, J. (2026). What drives precious metals pricing? An explainable mixed-frequency machine learning approach. Mineral Economics. https://doi.org/10.1007/s13563-025-00586-8
Xu, C., & Xie, Y. (2021). Conformal prediction interval for dynamic time-series. In Proceedings of the 38th International Conference on Machine Learning (Proceedings of Machine Learning Research, Vol. 139, pp. 11559–11569). https://proceedings.mlr.press/v139/xu21h.html
Ye, Y., Zhuang, X., Yi, C., Liu, D., & Tang, Z. (2025). Enhancing agricultural futures return prediction: Insights from rolling VMD, economic factors, and mixed ensembles. Agriculture, 15(11), 1127. https://doi.org/10.3390/agriculture15111127 (mdpi.com)
Ying, X., & Luo, B. (2025). Reducing forecast uncertainty in China’s gold futures market through mixed-frequency volatility modeling. Finance Research Letters, 86, 108898. https://doi.org/10.1016/j.frl.2025.108898
Juan, Z., Chong, C. W., Leong, Y. C., & Yihuan, L. (2026). Volatility Shock Regimes and Risk-Aware Forecasting of Silver Futures Returns: A Rolling Out-of-Sample Evaluation with Conformal Intervals. International Journal of Academic Research in Accounting, Finance and Management Sciences, 16(1), 288–304.
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