Conformal prediction for multi-dimensional time series by ellipsoidal sets

TL;DR

This paper introduces MultiDimSPCI, a conformal prediction method that constructs prediction regions for multivariate time series, providing valid coverage and smaller regions than existing methods.

Contribution

The paper develops a novel sequential conformal prediction method for multivariate time series that offers finite-sample coverage guarantees and improved efficiency.

Findings

Maintains valid coverage across various multivariate time series

Produces smaller prediction regions compared to baselines

Provides theoretical bounds on coverage gap

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 $\texttt{MultiDimSPCI}$ that builds prediction $\textit{regions}$ for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate $\textit{finite-sample}$ high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that $\texttt{MultiDimSPCI}$ maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.