Conformal PID Control for Time Series Prediction

TL;DR

This paper introduces a conformal PID control method for time series prediction that offers formal guarantees, adapts to distribution shifts, and improves uncertainty quantification across various forecasting tasks.

Contribution

It develops a novel conformal prediction framework integrated with control theory, enhancing online uncertainty quantification for time series with systematic errors.

Findings

Improved coverage in COVID-19 death forecasts

Effective adaptation to seasonality and trends

Versatile application across multiple forecasting models

Abstract

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.