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 computationally efficient algorithms, EnbPI, and SPCI, that wrap around ensemble predictors closely related to standard conformal prediction (CP) but do not require data exchangeability. Our algorithms avoid data-splitting and are computationally efficient by avoiding retraining and thus scalable to sequentially produce prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods.
