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Adaptive Conformal Inference for Multi-Step Ahead Time-Series Forecasting Online

Johan Hallberg Szabadváry

TL;DR

An adaptation of the well known adaptive conformal inference algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting is proposed, which suggests that a balance may be struck between efficiency and coverage.

Abstract

The aim of this paper is to propose an adaptation of the well known adaptive conformal inference (ACI) algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting. ACI dynamically adjusts significance levels, and comes with finite-sample guarantees on coverage, even for non-exchangeable data. Our multi-step ahead ACI procedure inherits these guarantees at each prediction step, as well as for the overall error rate. The multi-step ahead ACI algorithm can be used with different target error and learning rates at different prediction steps, which is illustrated in our numerical examples, where we employ a version of the confromalised ridge regression algorithm, adapted to multi-input multi-output forecasting. The examples serve to show how the method works in practice, illustrating the effect of variable target error and learning rates for different prediction steps, which suggests that a balance may be struck between efficiency (interval width) and coverage.t

Adaptive Conformal Inference for Multi-Step Ahead Time-Series Forecasting Online

TL;DR

An adaptation of the well known adaptive conformal inference algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting is proposed, which suggests that a balance may be struck between efficiency and coverage.

Abstract

The aim of this paper is to propose an adaptation of the well known adaptive conformal inference (ACI) algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting. ACI dynamically adjusts significance levels, and comes with finite-sample guarantees on coverage, even for non-exchangeable data. Our multi-step ahead ACI procedure inherits these guarantees at each prediction step, as well as for the overall error rate. The multi-step ahead ACI algorithm can be used with different target error and learning rates at different prediction steps, which is illustrated in our numerical examples, where we employ a version of the confromalised ridge regression algorithm, adapted to multi-input multi-output forecasting. The examples serve to show how the method works in practice, illustrating the effect of variable target error and learning rates for different prediction steps, which suggests that a balance may be struck between efficiency (interval width) and coverage.t
Paper Structure (9 sections, 15 equations, 3 figures, 3 tables)

This paper contains 9 sections, 15 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Multi-step ahead time-series forecasting
  3. MIMO conformalised ridge regression
  4. Multi-step ahead adaptive conformal inference
  5. Example: electricity demand forecast
  6. Same target coverage and learning rate for all
  7. Different target coverage but same learning rate
  8. Different target coverage and learning rates
  9. Conclusions

Figures (3)

  • Figure 1: Example 1. Same target coverage rate and learning rate for all predictions.
  • Figure 2: Example 2. Different target error rates for different forecast hours, but same learning rate. Note the difference in scale on the $y$-axis compared to Figure \ref{['fig:same_eps_same_gam_control']}.
  • Figure 3: Example 3. Different target coverage and learning rates for different forecast hours. Note the difference in scale on the $y$-axis compared to \ref{['fig:same_eps_same_gam_control']}.