Conformal multistep-ahead multivariate time-series forecasting

Abstract Time-series forecasts underpin decision-making processes in a wide range of application domains. Recently it has been shown that these processes can be strengthened by conformal prediction, a framework that allows adding prediction intervals to point forecasts. The prediction intervals quantify the uncertainty of a predictive model with mathematical coverage guarantees, giving the user a range of scenarios to consider. However, applying conformal prediction to time-series tasks is not trivial. This is either because the exchangeability condition the framework places on the data is violated, or because the framework only allows for one-step-ahead univariate forecasts. In this article we combine two existing methods derived from conformal prediction, one built for multi-target regression and one designed to handle non-exchangeable data. The resulting method, called non-exchangeable multi-target conformal prediction (nmtCP) produces provably robust prediction regions for multi-step ahead multidimensional time-series forecasts, meaning that the miscoverage rate is bound. Additionally, nmtCP is computationally efficient and easy to implement. Due to its model-agnostic nature, nmtCP can be used on top of any time-series model that produces point forecasts. A theoretical analysis proves the method’s robustness while experiments on real-world data sets give insights into its practical behavior and performance.