Testing for threshold effects in the TARMA framework

TL;DR

This paper develops supremum Lagrange Multiplier tests to detect threshold effects in ARMA models, providing theoretical derivations, simulation evidence, and an application to climate data.

Contribution

It introduces new supremum Lagrange Multiplier tests for threshold effects in ARMA models, with proven asymptotic properties and robustness, applicable even when model order is unknown.

Findings

Tests have good finite-sample performance

Tests are robust against model mis-specification

Application to climate data demonstrates practical utility

Abstract

We present supremum Lagrange Multiplier tests to compare a linear ARMA specification against its threshold ARMA extension. We derive the asymptotic distribution of the test statistics both under the null hypothesis and contiguous local alternatives. Moreover, we prove the consistency of the tests. The Monte Carlo study shows that the tests enjoy good finite-sample properties, are robust against model mis-specification and their performance is not affected if the order of the model is unknown. The tests present a low computational burden and do not suffer from some of the drawbacks that affect the quasi-likelihood ratio setting. Lastly, we apply our tests to a time series of standardized tree-ring growth indexes and this can lead to new research in climate studies.