Conformal Time Series

The core mechanism for handling temporal dependence. Instead of a static calibration set, a rolling window of the most recent observations is used to compute nonconformity scores. This ensures the calibration data reflects the current data-generating process, mitigating the impact of distribution drift. The window size is a critical hyperparameter: too small yields high variance, too large retains stale patterns.

An online learning approach that dynamically adjusts the conformal quantile in response to observed errors. When coverage drops below the target, ACI increases the threshold to widen intervals; when coverage exceeds the target, it decreases the threshold to tighten them. A learning rate parameter controls the speed of adaptation, providing long-run coverage guarantees without any distributional assumptions.

A method that combines bootstrap ensemble models with conformal calibration for time series. EnbPI trains an ensemble of base forecasters on bootstrapped samples, then uses the empirical distribution of leave-one-out residuals as nonconformity scores. This captures model uncertainty and residual noise simultaneously, producing tighter intervals than methods that rely on a single point forecaster.

Applies exponential decay weights to calibration residuals, giving higher importance to recent observations. The weight function is defined as w_i = exp(-λ(t - i)), where λ controls the decay rate. This provides a smooth alternative to hard window cutoffs and is particularly effective when the rate of distribution shift varies over time.

Extends conformal guarantees to forecasting multiple steps ahead simultaneously. A separate nonconformity score is computed for each horizon h, and a joint prediction region is constructed using a Bonferroni correction or a max-score aggregation. This ensures the entire forecast trajectory is covered with the specified probability, critical for trajectory planning and inventory management.

Wraps deep learning forecasters like Temporal Fusion Transformers with a conformal calibration layer. The model's quantile outputs are treated as base intervals, and a held-out calibration period corrects for any miscalibration. This combines the representational power of attention-based architectures with finite-sample coverage guarantees, bridging the gap between deep learning and rigorous uncertainty quantification.