Adaptive Conformal Predictions for Time Series (2202.07282v1)

Abstract: Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works tackled this issue, we argue that Adaptive Conformal Inference (ACI, Gibbs and Cand{`e}s, 2021), developed for distribution-shift time series, is a good procedure for time series with general dependency. We theoretically analyse the impact of the learning rate on its efficiency in the exchangeable and auto-regressive case. We propose a parameter-free method, AgACI, that adaptively builds upon ACI based on online expert aggregation. We lead extensive fair simulations against competing methods that advocate for ACI's use in time series. We conduct a real case study: electricity price forecasting. The proposed aggregation algorithm provides efficient prediction intervals for day-ahead forecasting. All the code and data to reproduce the experiments is made available.

• The paper demonstrates that Adaptive Conformal Inference (ACI) improves uncertainty quantification by adapting to temporal dependencies and distribution shifts.
• It introduces AgACI, a parameter-free method using online expert aggregation, which selects optimal learning rates without heuristic tuning.
• Empirical evaluations on synthetic ARMA processes and French electricity price data validate the method’s robust interval coverage and efficiency.

Overview of Adaptive Conformal Predictions for Time Series

The paper, "Adaptive Conformal Predictions for Time Series," presents a refined approach to uncertainty quantification in decision-making problems concerning time series data. In particular, the authors explore a specialized version of conformal prediction (CP), termed Adaptive Conformal Inference (ACI), tailored for handling dependent and distribution-shift-prone time series data. This essay provides a concise and detailed summary of the contributions, evaluations, and implications outlined in the paper.

The central need addressed by this paper is the requirement for effective uncertainty quantification in predictive models used within volatile and dependent markets, such as electricity price forecasting. The paper highlights the limitations of traditional CP methods, which demand exchangeable data—an assumption not typically met in time series. To address this, the paper builds on the adaptive nature of ACI, originally introduced for situations of adversarial distribution shifts, and tweaks it to be suitable for time series data with general temporal dependencies.

Key Contributions and Numerical Experiments

The paper makes several notable contributions:

1. Theoretical Analysis: The authors provide an extensive theoretical analysis of ACI, focusing on the role of the learning rate ($\gamma$) in fostering efficient predictive intervals within dependent data contexts. It is demonstrated that a well-tuned $\gamma$ can improve interval efficiency in autoregressive scenarios, while it may cause deterioration in efficiency for exchangeable data.
2. Introduction of AgACI: A parameter-free variation, AgACI, is proposed. This method leverages online expert aggregation to adaptively select the best $\gamma$, avoiding the critical and often heuristic choice of a fixed learning rate.
3. Synthetic Data Evaluations: Comprehensive experiments on synthetic data sets—parameterized over various ARMA processes—highlight the effectiveness of ACI and its derivatives compared to standard alternatives like EnbPI and sequential split CP methods. AgACI consistently achieved close to nominal coverage while maintaining efficient interval lengths.
4. Real-World Case Study: Applying ACI-based methods to real-world French electricity price data reinforces the practical applicability of these techniques, showcasing their ability to predict informative intervals aligning with market behaviors.

Implications and Future Directions

The adaptation of ACI for time series augments the versatility of conformal prediction beyond traditional constraints, enabling its deployment in time-dependent settings without sacrificing theoretical robustness. The use of online expert aggregation in AgACI marks a promising direction for future work, possibly extending beyond time series to other domains facing similar dependency structures.

The theoretical findings, explicitly characterizing the impact of the learning rate $\gamma$, address a critical gap between applicability and statistical assurance in dependent data settings. Open questions remain on generalizing this adaptive method, particularly its theoretical properties vis-a-vis varying temporal structures beyond AR processes, which could significantly broaden its utility.

Overall, the paper highlights seminal steps toward adaptive interval predictions in non-exchangeable data contexts, showcasing both methodological soundness and practical efficacy through rigorous empirical validation. The work stands as a robust foundation for advancing uncertainty quantification strategies in financial forecasting, energy markets, and other domains dealing with intricate time-dependent datasets.