SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting

2026-08-17

AI Summary

SPACE方法通过从当前预测样本云估计时间局部协方差几何并动态调整回溯窗口来构建椭球联合预测区域，以解决多变量时间序列预测中的不确定性量化问题。

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.

Problem

• forecast samples
• coverage guarantees
• distribution shift
• conformal methods
• covariance geometry

Innovation

• conformal prediction
• multivariate time-series forecasting
• dynamic window selection
• ellipsoidal prediction regions
• covariance geometry