Conformal PID Control for Time Series Prediction
Anastasios N. Angelopoulos Emmanuel J. Candes Ryan J. Tibshirani
We study the problem of uncertainty quantification for time series
prediction, with the goal of providing easy-to-use algorithms with formal
guarantees. The algorithms we present build upon ideas from conformal
prediction and control theory, are able to prospectively model conformal scores
in an online setting, and adapt to the presence of systematic errors due to
seasonality, trends, and general distribution shifts. Our theory both
simplifies and strengthens existing analyses in online conformal prediction.
Experiments on 4-week-ahead forecasting of statewide COVID-19 death counts in
the U.S. show an improvement in coverage over the ensemble forecaster used in
official CDC communications. We also run experiments on predicting electricity
demand, market returns, and temperature using autoregressive, Theta, Prophet,
and Transformer models. We provide an extendable codebase for testing our
methods and for the integration of new algorithms, data sets, and forecasting
rules.