Hidden Coverage Failures in Bitcoin Volatility Prediction Intervals Across Sentiment States

Prediction intervals are commonly evaluated using aggregate coverage and average width, but these summaries can conceal failures concentrated in specific market conditions. This study examines whether seven-day-ahead Bitcoin volatility intervals with apparently adequate global calibration remain reliable across Fear, Neutral, and Greed sentiment states.

Intervals are evaluated at a nominal 95% coverage level across 24 chronological walk-forward test windows and three volatility measures: realized, Garman-Klass, and Rogers-Satchell volatility. Raw quantile, symmetric conformal, and conformalized quantile regression (CQR) intervals are compared across econometric, tree-based, LSTM, and GRU forecasters. Sentiment states are defined at the forecast origin using the Alternative.me Crypto Fear & Greed Index (Fear ≤ 33, Neutral 34–66, and Greed ≥ 67). Robustness is assessed using non-overlapping forecast origins, block-bootstrap confidence intervals, and multiple neural-network seeds.

For Garman-Klass volatility, a HAR-OLS raw-quantile interval using only price and volume information achieves 94.58% pooled coverage but only 89.36% during Fear, 5.64 percentage points below the nominal level; overcoverage in Neutral and Greed partly offsets this shortfall. The Fear-state undercoverage remains visible under non-overlapping-origin and block-bootstrap diagnostics. Among intervals with pooled coverage within 0.5 percentage points of the nominal 95% level, the smallest maximum absolute state-specific coverage errors are obtained by an LSTM with regime-specific CQR for realized volatility, a GRU with standard CQR for Garman-Klass volatility, and a GRU with regime-specific CQR for Rogers-Satchell volatility. Regime-specific calibration improves selected cases but not consistently, with gains sometimes smaller than random-seed variation.

Market-state conditioning is therefore most useful as a diagnostic stress test rather than as a universal calibration rule. Evaluating coverage across sentiment states can expose failures hidden by pooled validation and distinguish more balanced interval specifications, while lower- and upper-tail miss rates, temporal dependence, and seed stability provide additional evidence on forecast reliability.