Conformal prediction for time series

About

We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We obtain similar bounds on the size of set differences between oracle and estimated prediction intervals. Methodologically, we introduce a computationally efficient algorithm called \texttt{EnbPI} that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. \texttt{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. We also discuss the extension of \texttt{EnbPI} on various other applications.

Chen Xu, Yao Xie · 2020

Related benchmarks

Task	Dataset	Result
Prediction Interval Estimation	Sap flow	Delta Cov-0.006	39
Prediction Interval Estimation	Air 10 PM	Delta Cov-0.002	39
Prediction Interval Estimation	Air 25 PM	Delta Cov-0.003	39
Time Series Conformal Prediction	Solar 3Y (test)	Delta Covariance-0.001	19
Uncertainty Estimation	Solar 1Y (test)	$Δ$ Cov-0.002	8
Conformal Prediction	Streamflow alpha=0.05 (test)	Δ Cov-0.042	7
Conformal Prediction	Streamflow alpha=0.10 (test)	Delta Cov-0.054	7
Conformal Prediction	Streamflow alpha=0.15 (test)	Delta Coverage-6.1	7
Conformal Prediction	CALCE FUDS (in-distribution)	Coverage94.998	2
Conformal Prediction	CALCE US06 45°C real shift (out-of-distribution)	Coverage70.129	2