Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

• URL: http://arxiv.org/abs/2402.05203v2
• Date: Fri, 9 Feb 2024 16:47:02 GMT
• Title: Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series
• Authors: Zitong Yang, Emmanuel Cand\`es, Lihua Lei
• Abstract summary: We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models. BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence.
• Score: 4.10373648742522
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides approximately calibrated prediction intervals. Unlike existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. We find empirically that BCI avoids uninformative intervals that have infinite lengths and generates substantially shorter prediction intervals in multiple applications when compared with existing methods.

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