Self-normalized tests for multistep conditional predictive ability

TL;DR

This paper introduces self-normalized tests for multistep forecast comparison that avoid complex covariance estimation, offering more reliable size control and strong power in finite samples.

Contribution

It develops a novel self-normalized testing approach for multistep predictive ability that eliminates the need for bandwidth and lag-truncation choices, with proven asymptotic properties.

Findings

The tests effectively reduce finite-sample size distortions compared to HAC methods.

They maintain strong empirical power against predictability alternatives.

Asymptotic theory confirms the tests' pivotal null distributions.

Abstract

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process, specifically an adjusted-range normalizer for scalars and a matrix normalizer for vectors, our approach avoids direct estimation of the long-run covariance matrix. Consequently, it eliminates the need for the ad hoc bandwidth, kernel, and lag-truncation choices required by traditional methods. We establish the asymptotic theory for these statistics, deriving pivotal null limiting distributions and proving test consistency. Monte Carlo simulations show that the proposed tests effectively mitigate the finite-sample size distortions associated with traditional heteroskedasticity and autocorrelation consistent (HAC) methods, while retaining strong empirical power against conditional predictability alternatives.