Conformal prediction interval for dynamic time-series

We develop a method to build distribution-free prediction intervals for time-series based on conformal inference, called \Verb|EnPI| that wraps around any ensemble estimator to construct sequential prediction intervals. \Verb|EnPI| is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain finite-sample, approximately valid average coverage for broad classes of regression functions and time-series with strongly mixing stochastic errors. Computationally, \Verb|EnPI| requires no training of multiple ensemble estimators; it efficiently operates around an already trained ensemble estimator. In general, \Verb|EnPI| 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 simulations and real-data analyses to demonstrate its effectiveness.