  Conformal Inference (CI) is a popular approach for generating finite sample
prediction intervals based on the output of any point prediction method when
data are exchangeable. Adaptive Conformal Inference (ACI) algorithms extend CI
to the case of sequentially observed data, such as time series, and exhibit
strong theoretical guarantees without having to assume exchangeability of the
observed data. The common thread that unites algorithms in the ACI family is
that they adaptively adjust the width of the generated prediction intervals in
response to the observed data. We provide a detailed description of five ACI
algorithms and their theoretical guarantees, and test their performance in
simulation studies. We then present a case study of producing prediction
intervals for influenza incidence in the United States based on black-box point
forecasts. Implementations of all the algorithms are released as an open-source
R package, AdaptiveConformal, which also includes tools for visualizing and
summarizing conformal prediction intervals.
