What question did this study set out to answer?

To develop a framework for forecasting silver futures returns while evaluating risk across different volatility regimes.

February 21, 2026Open Access

Volatility Shock Regimes and Risk-Aware Forecasting of Silver Futures Returns: A Rolling Out-of-Sample Evaluation with Conformal Intervals

Key Points

To develop a framework for forecasting silver futures returns while evaluating risk across different volatility regimes.
Developed a regime-conditioned forecasting framework using daily silver futures data from 2010 to 2026.
Used log returns and a realized-volatility proxy to identify shock regimes via a rolling quantile threshold.
Benchmark models include random-walk, linear ARX models, and gradient-boosted trees, evaluated out-of-sample.
Incorporated macroeconomic variables aligned to daily observations, analyzing their contributions while avoiding look-ahead bias.
Constructed online rolling conformal prediction intervals to assess uncertainty during different shock regimes.
Strong benchmarks are challenging to outperform in RMSE during volatility shocks.
Directional accuracy is horizon-dependent, with linear models performing better in the short term and non-linear models more stable in the long term.
Macro variables do not significantly enhance predictive accuracy compared to strong benchmarks after accounting for risk.
Conformal intervals widen during shocks, but coverage decreases in stress states, indicating the potential for operational triggers.

Abstract

HRMARS - 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.

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