Conformal prediction for multi-dimensional time series by ellipsoidal sets
This addresses uncertainty quantification for multivariate time series forecasting, an incremental advance over existing univariate methods.
The paper tackled the problem of uncertainty quantification for multivariate time series forecasting by developing a sequential conformal prediction method called MultiDimSPCI, which builds prediction regions and achieves valid coverage with smaller regions than baselines.
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.