Regime-Aware Conformal Aggregation for Calibrated Return Intervals and Value-at-Risk in Financial Markets

Abstract

Machine-learning studies of financial markets often report high price-level accuracy from a single market, using point predictions without a random-walk comparison or any check that their uncertainty is reliable. We study the calibration of prediction intervals and value-at-risk (VaR) for daily returns under a leakage-controlled protocol, using 34 assets across equity indices, foreign exchange, commodities and cryptocurrencies (2000–2026) and a confirmation tier of 162 S&P 500 stocks. Eight quantile models, ranging from historical simulation and GJR-GARCH to LightGBM, an LSTM network and two ensembles, produced 90% intervals for one- and five-day returns. These intervals were calibrated with eleven conformal methods, including recent financial and tail-specific proposals, aggregated adaptive conformal inference (AgACI), and a new regime-aware aggregation (RA-AgCI) that learns which calibrator to trust in each real-time market regime. Evaluation used purged walk-forward cross-validation over five crisis-spanning folds, an untouched 2025–2026 hold-out, Holm-corrected Wilcoxon and paired t-tests, Diebold–Mariano tests, the model confidence set, VaR backtests and explainable AI. Common evaluation shortcuts mattered more than any model: smoothing the series before splitting raised the out-of-sample R^2 of daily return predictions from -0.9% to 46.8%, and a random walk matched every model on price-level R^2 (0.994). No model predicted the direction of returns, but every learned model described the return distribution better than historical simulation (p<0.001), with an online quantile-weighted ensemble performing best (5.7% lower pinball loss in cross-validation and 5.2% on the hold-out). For one-day intervals, RA-AgCI gave the lowest interval score on all three base models and the highest VaR-backtest pass rates (97–100% of assets), significantly improving on ACI and tail-specific ECI but not on global aggregation. Gains were below 1%, did not extend to five days, and ACI retained the smallest per-asset coverage error. On the stock tier, RA-AgCI performed best with GARCH and historical-simulation bases but not with LightGBM. Regime information is therefore most useful for models that do not adapt to volatility, and rigorous validation matters more than model choice.