Conformal prediction for time series

We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We obtain similar bounds on the size of set differences between oracle and estimated prediction intervals. Methodologically, we introduce a computationally efficient algorithm called \texttt{EnbPI} that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. \texttt{EnbPI} avoids data-splitting and is computationally efficient by avoiding retraining and thus scalable to sequentially producing prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods. We also discuss the extension of \texttt{EnbPI} on various other applications.