  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.
