Conformal prediction interval for dynamic time-series

We develop a method to construct distribution-free prediction intervals for dynamic time-series, called EnbPI that wraps around any bootstrap ensemble estimator to construct sequential prediction intervals. EnbPI is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain asymptotically valid marginal coverage for broad classes of regression functions and time-series with certain dependencies. Intervals also converge in width to the oracle lower bound asymptotically. Computationally, EnbPI avoids overfitting and requires neither data-splitting nor training multiple ensemble estimators; it efficiently aggregates bootstrap estimators that have been trained. In general, EnbPI is easy to implement, scalable to producing arbitrarily many prediction intervals sequentially, and well-suited to a wide range of regression functions. We perform extensive simulation and real-data analyses to demonstrate its effectiveness and applicability beyond predictive inference.