Conformal PID Control for Time Series Prediction
This work addresses the problem of providing reliable uncertainty estimates for time series forecasting, which is crucial for applications like public health and energy management, though it is incremental in building on existing conformal prediction techniques.
The paper tackles uncertainty quantification for time series prediction by developing algorithms that combine conformal prediction and control theory, resulting in improved coverage in forecasting COVID-19 death counts compared to official CDC methods.
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.