Temporal Conformal Prediction (TCP): Rolling Calibration for Financial Risk Forecasting

We study two rolling conformal procedures that construct prediction intervals for financial returns. Temporal Conformal Prediction (TCP) uses a zero-truncated version of the conformalized quantile regression (CQR) score. TCP-RM adds an offset updated from observed coverage errors with a decaying step size. We compare ten forecasting methods and two diagnostic controls across thirteen financial series on 1,448 common forecast dates. The nominal interval coverage is 95%. TCP attains coverage of 95.23% for the S&P 500, 95.37% for Bitcoin and 94.27% for Gold. Across all thirteen series, CQR has the smallest mean absolute deviation from the coverage target, followed by TCP and TCP-RM. TCP and CQR produce different intervals on 3.655% of forecasts. TCP-RM changes coverage and width little at the main settings. Coverage and interval score give different rankings. In 52 paired interval-score comparisons between TCP and four volatility-based benchmarks, 42 favour the volatility model and ten show no significant difference. These are individual Diebold--Mariano tests at the 5% level without a multiple-testing adjustment. Crisis-window results vary across markets, and good full-sample interval coverage does not ensure lower-tail calibration. The standard split-conformal guarantee requires exchangeability and does not automatically apply to the dependent returns evaluated here. The results support evaluating rolling conformal forecasts through coverage, interval scores and separate tail diagnostics, rather than closeness to the coverage target alone.