Conformal Prediction Interval for Dynamic Time Series

Chen Xu, Yao Xie

Abstract:

We develop a method to construct distributionfree 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.