Empirical likelihood-based portmanteau tests for autoregressive moving average models with possible infinite variance innovation

TL;DR

This paper introduces two empirical likelihood-based portmanteau tests for ARMA models, addressing size distortion issues especially with low persistence and infinite variance innovations, validated through simulations and real data.

Contribution

It proposes novel empirical likelihood-based portmanteau tests for ARMA models, including a version for infinite variance innovations, with derived asymptotic distributions.

Findings

Tests perform well in simulations

Effective for models with low persistence

Applicable to data with infinite variance innovations

Abstract

It is an important task in the literature to check whether a fitted autoregressive moving average (ARMA) model is adequate, while the currently used tests may suffer from the size distortion problem when the underlying autoregressive models have low persistence. To fill this gap, this paper proposes two empirical likelihood-based portmanteau tests. The first one is naive but can serve as a benchmark, and the second is for the case with infinite variance innovations. The asymptotic distributions under the null hypothesis are derived under mild moment conditions, and their usefulness is demonstrated by simulation experiments and two real data examples.