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 finite-sample, approximately valid marginal coverage for broad classes of regression functions and time-series with strongly mixing stochastic errors. 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 real-data analyses to demonstrate its effectiveness.