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Conformal prediction for multi-dimensional time series by ellipsoidal sets

Chen Xu · Hanyang Jiang · Yao Xie

Hall C 4-9 #1707

Abstract: Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called MultiDimSPCI that builds prediction regions for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate finite-sample high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that MultiDimSPCI maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.

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