[Paper Review] Conformal prediction for dynamic time-series.

Chen Xu, Yao Xie|arXiv (Cornell University)|Oct 18, 2020

Time Series Analysis and Forecasting49 references4 citations

TL;DR

This paper introduces EnbPI, a computationally efficient, distribution-free method for constructing prediction intervals in dynamic time series without requiring data exchangeability or data splitting. It asymptotically achieves valid conditional and marginal coverage while converging to the width of the oracle interval, outperforming existing methods in simulation and real-data studies.

ABSTRACT

We develop a general framework constructing distribution-free prediction intervals for dynamic time series. We show that our intervals asymptotically attain valid conditional and marginal coverages for a broad class of predictions functions and time series. We also show that our interval width converges to that of the oracle prediction interval asymptotically. Moreover, we introduce a computationally efficient algorithm called \verb|EnbPI| that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. \verb|EnbPI| avoids data-splitting and is computationally efficient by avoiding retraining and thus scalable to sequentially producing prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods.

Motivation & Objective

• To develop a distribution-free framework for constructing prediction intervals in dynamic time series that ensures valid coverage without assuming data exchangeability.
• To enable scalable, real-time prediction interval generation by avoiding data splitting and retraining.
• To achieve asymptotic convergence of interval width to that of the oracle interval under broad conditions.
• To design a computationally efficient algorithm compatible with ensemble predictors for practical deployment.

Proposed method

• The method introduces EnbPI, a wrapper algorithm that applies conformal prediction principles to ensemble predictors without requiring exchangeability of time series data.
• It constructs prediction intervals using residuals from a rolling window of past predictions, enabling sequential interval generation.
• The framework ensures asymptotic validity of both marginal and conditional coverage under weak regularity conditions on the prediction function and time series.
• By avoiding retraining and data splitting, EnbPI achieves computational efficiency suitable for large-scale or streaming time series.
• The approach leverages ensemble predictors as base learners, allowing flexibility and robustness in complex, non-i.i.d. time series settings.

Experimental results

Research questions

• RQ1 Can a conformal prediction method be designed for time series that does not rely on data exchangeability?
• RQ2 Can such a method achieve asymptotically valid conditional and marginal coverage in dynamic settings?
• RQ3 Can the prediction interval width converge to that of the oracle interval under general conditions?
• RQ4 Is it possible to construct a scalable, real-time algorithm that avoids data splitting and retraining?

Key findings

• EnbPI achieves asymptotically valid conditional and marginal coverage for a broad class of prediction functions and time series models.
• The width of the prediction intervals constructed by EnbPI converges asymptotically to that of the oracle interval, indicating optimal interval size.
• The method is computationally efficient, avoiding data splitting and retraining, enabling scalable sequential prediction interval generation.
• Empirical evaluations on simulations and real-world data show EnbPI outperforms existing methods in coverage validity and interval sharpness.