A model sufficiency test using permutation entropy

TL;DR

This paper introduces a permutation entropy-based model sufficiency test that better assesses point prediction accuracy, especially when innovations have structured dependencies, addressing limitations of classical tests.

Contribution

It proposes a novel sufficiency test using permutation entropy that remains valid with structured innovations, improving upon classical methods like Broock et al.'s test.

Findings

The new test is more accurate with structured innovations.

It reduces false conclusions about model sufficiency.

It aligns model evaluation with prediction accuracy.

Abstract

Using the ordinal pattern concept in permutation entropy, we propose a model sufficiency test to study a given model's point prediction accuracy. Compared to some classical model sufficiency tests, such as the Broock et al.'s (1996) test, our proposal does not require a sufficient model to eliminate all structures exhibited in the estimated residuals. When the innovations in the investigated data's underlying dynamics show a certain structure, such as higher-moment serial dependence, the Broock et al.'s (1996) test can lead to erroneous conclusions about the sufficiency of point predictors. Due to the structured innovations, inconsistency between the model sufficiency tests and prediction accuracy criteria can occur. Our proposal fills in this incoherence between model and prediction evaluation approaches and remains valid when the underlying process has non-white additive innovation.