Conformal prediction for multi-dimensional time series by ellipsoidal
  sets
Chen Xu Hanyang Jiang Yao Xie
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 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 $\texttt{MultiDimSPCI}$ maintains valid
coverage on a wide range of multivariate time series while producing smaller
prediction regions than CP and non-CP baselines.