Conformal Prediction for Multivariate Time Series Forecasting Under Heterogeneous Distribution Shifts

$\text{Conformal prediction on multivariate time series forecasting}$ provides intervals that cover true values with high probability, supporting reliable decision-making under uncertainty. Existing sequential conformal methods typically target marginal coverage across all components and rely on the assumption that calibration and future forecast data have a joint distribution invariant under reordering. However, distribution shifts are common in time series, violating this invariance assumption, and can furthermore be heterogeneous across components in multivariate settings, leading to component-specific coverage failures. In this paper, we propose $\text{Boundary-aware Conformal Recalibration}$ (BaCR), which combines two complementary mechanisms: $\text{a unified recalibrator}$ that periodically adapts the quantile estimates used to construct prediction intervals, and $\text{component-wise trackers}$ that provide immediate online interval correction within the finite range supported by these quantile estimates and report a signal when additional expansion is needed. Theoretically, we derive an exact decomposition of component-wise empirical coverage error that characterizes tracker correction and the boundary limitations from the conditional quantile estimates. Experiments on a synthetic benchmark and four real-world datasets show that BaCR substantially reduces component-wise undercoverage, especially on large-shift components, and produces more efficient intervals compared to baselines.