We present a general framework for constructing distribution-free prediction intervals for time series. We establish explicit bounds on the conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We also provide similar bounds on the size of set differences between oracle and estimated prediction intervals. To implement this framework, we introduce an efficient algorithm called EnbPI, which utilizes ensemble predictors and is closely related to conformal prediction (CP) but does not require data exchangeability. Unlike other methods, EnbPI avoids data-splitting and is computationally efficient by avoiding retraining, making it scalable for sequentially producing prediction intervals. Extensive simulation and real-data analyses demonstrate the effectiveness of EnbPI compared to existing methods.
