Information criteria for multistep ahead predictions

TL;DR

This paper introduces an information criterion tailored for multistep ahead predictions, demonstrating its effectiveness through theoretical derivation and numerical experiments, especially under local model misspecification.

Contribution

It develops a novel information criterion for multistep ahead predictions based on asymptotic properties of Bayesian predictive distributions.

Findings

Bayesian predictive distributions outperform plug-in methods in KL risk.

The proposed criterion is asymptotically unbiased for multistep predictions.

Numerical experiments confirm the criterion's effectiveness.

Abstract

We propose an information criterion for multistep ahead predictions. It is also used for extrapolations. For the derivation, we consider multistep ahead predictions under local misspecification. In the prediction, we show that Bayesian predictive distributions asymptotically have smaller Kullback--Leibler risks than plug-in predictive distributions. From the results, we construct an information criterion for multistep ahead predictions by using an asymptotically unbiased estimator of the Kullback--Leibler risk of Bayesian predictive distributions. We show the effectiveness of the proposed information criterion throughout the numerical experiments.