Sequential Predictive Conformal Inference for Time Series
This work addresses the need for reliable uncertainty quantification in time series forecasting, which is incremental as it adapts conformal prediction to handle temporal dependence.
The paper tackles the problem of generating distribution-free prediction intervals for non-exchangeable time series data, where existing conformal prediction methods are not applicable, by introducing a sequential predictive conformal inference algorithm that reduces interval width while maintaining empirical coverage.
We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of \texttt{SPCI} compared to other existing methods under the desired empirical coverage.