SPACE is proposed, a conformal wrapper for sample-generating multivariate forecasters that consistently brings realized joint and rolling coverage closer to the nominal target, achieving superior coverage-efficiency tradeoffs relative to competing wrappers.
Abstract
Modern probabilistic time-series forecasters often express uncertainty through forecast samples. While typically converted into nominal prediction regions using empirical quantiles, these model-implied sets lack formal coverage guarantees and frequently deviate from nominal targets under distribution shift. Existing multivariate conformal methods can calibrate these regions online, but they typically estimate geometry from historical residuals using fixed or accumulating look-back windows. This reliance on the past limits their ability to exploit the instantaneous dependence structure of current predictions and leaves them vulnerable to stale-regime contamination. To address this, we propose SPACE, a conformal wrapper for sample-generating multivariate forecasters. SPACE constructs ellipsoidal joint prediction regions by estimating time-local covariance geometry directly from the current forecast sample cloud, calibrating the region's radius via a dynamic backward window-selection scheme. Across diverse multivariate datasets, probabilistic forecasters, and conformal baselines, SPACE consistently brings realized joint and rolling coverage closer to the nominal target, achieving superior coverage-efficiency tradeoffs relative to competing wrappers.
We propose ABF-T-GLCP, a model-agnostic framework for forecasting and uncertainty quantification in nonstationary multivariate time series. The central idea is to learn an adaptive predictive state representation for point forecasting and reuse it for conformal calibration. The forecasting module combines horizon-specific temporal experts through a learned gate and refines predictions using sparse predictive transfer across related series. The uncertainty module, Gate-Localized Conformal Prediction (GLCP), uses the learned gate state, together with temporal recency, to select locally relevant calibration residuals, thereby coupling uncertainty calibration to the predictive regimes used by the forecasting model. This shared representation allows point forecasts and prediction intervals to adapt consistently under evolving temporal dynamics while retaining the model-agnostic nature of conformal prediction and yielding approximate local coverage under mild stability conditions. Experiments on a large-scale high-frequency commodity forecasting benchmark show consistent gains in point forecasting accuracy and substantially narrower prediction intervals with empirical coverage close to the nominal level. Additional results indicate that the framework extends beyond the motivating financial application.
Ziling Ma, Junshu Jiang, Ángel López-Oriona et al.· 0 citations
The proposed Dynamic Regime-Aware Conformal Prediction (DRACP), which combines density-ratio, localized kernel and probabilistic regime-aware weighting with a self-tuning online significance controller in a unified weighted conformal calibration framework, provides the most reliable calibration.
Online conformal prediction methods such as Adaptive Conformal Inference (ACI) and Fully Adaptive Conformal Inference (FACI) adjust prediction intervals under distribution shift, but their calibration is based on a common stream of recent nonconformity scores. We introduce Population-based Adaptive Conformal Ensembles (PACE), a heuristic method that maintains online conformal quantile calibrators with different window sizes, decay rates, and quantile scales. PACE combines the best-calibrated members through fitness-weighted top-K averaging and periodically refreshes the population using clonal selection. For context, Strongly Adaptive Online Conformal Prediction (SAOCP) is a benchmark method that combines online calibration experts operating over different time intervals and provides a formal strongly adaptive regret guarantee. PACE is heuristic and does not provide an analogous regret or coverage guarantee. We evaluate the method on two synthetic datasets and three real-world time series. Against five adaptive conformal baselines, PACE achieves higher empirical coverage during extreme regimes. Compared with SAOCP, it generally obtains higher coverage by producing wider intervals, resulting in less favorable interval scores on most datasets.
Marzieh Amiri Shahbazi, Ali Baheri· Forecasting· 0 citations
Probabilistic long-term time-series forecasting commonly relies on trained models. Training-free conformal methods typically construct intervals around a pre-existing point forecaster and do not natively represent a complete predictive distribution; sequential variants additionally suffer from increasingly delayed feedback at long horizons. We propose KReF, a training-free retrieval framework that treats retrieved historical futures as a querylocal empirical predictive distribution. After robust preprocessing, KReF embeds each lookback using handcrafted statistics or frozen random Fourier features and retrieves similar historical lookback-future pairs. Their similarity weights directly define predictive masses, quantiles, CRPS, and a weighted-mean point forecast. KReF further uses the observed query lookback to construct a probability-integral-transform map and applies validation-selected expansion and shrinkage rates to adapt interval boundaries. Across six LTSF benchmarks and four horizons, KReF obtains the lowest CRPS in all 12 dataset-embedding settings and the lowest IS90 in 9 settings. Without gradient-based fitting, its point forecasts also match or surpass trained baselines on two of six datasets. An archive-oracle analysis further reveals substantial headroom under finer horizon- and channel-wise routing. These results establish retrieval as a useful and underexplored inductive bias for LTSF.
Reliable financial forecasting requires not only accurate point predictions but calibrated uncertainty that remains valid under market stress. Conformal prediction offers distribution-free, finite-sample coverage guarantees and has recently been applied to risk-adjusted financial models, yet existing approaches calibrate each asset in isolation. Per-asset calibration is statistically inefficient, degrades sharply when historical data are scarce, and yields poor conditional coverage precisely when it matters most, that is, during volatile and highly correlated market regimes. We propose Cross-Asset Graph Conformal Prediction (CA-GCP), a framework that pools volatility-normalized nonconformity scores across the correlation-graph neighborhood of each target asset using a proximity- and recency-weighted quantile, grounded in the theory of weighted conformal prediction. A lightweight systemic-stress modulator further widens intervals on days of market-wide turbulence. On five years of daily returns for 100 S&P 500 constituents, CA-GCP reduces the cross-sectional standard deviation of per-asset coverage from 1.55% to 0.96% and improves worst-decile coverage from 91.4% to 94.1% relative to a faithful re-implementation of a state-of-the-art per-asset volatility-adaptive conformal baseline, while achieving 95.2% coverage on extreme-volatility days versus 90.4%. Under severe calibration scarcity, with as few as 20 samples per asset, CA-GCP maintains a coverage standard deviation below 0.9%, four to five times more stable than per-asset methods. The gains are robust across graph topologies and forecasting backbones, indicating that cross-asset pooling, rather than any particular graph, is the source of improvement. CA-GCP is model-agnostic, adds negligible computational overhead, and comes with finite-sample validity bounds.
