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.

翻译：我们提出直线ARMA规格与ARMA阈值扩展值比较的超模拉格朗多比器测试。我们从无效假设和毗连的当地替代物中得出测试统计数据的无症状分布。此外,我们证明测试的一致性。蒙特卡洛研究显示,测试具有良好的有限抽样特性,在模型的顺序不明的情况下,测试对模型的误差具有很强的抗力,其性能不会受到影响。测试呈现低计算负担,不会受到影响准相似比率设定的一些缺陷的影响。最后,我们将测试应用于一个标准化树环生长指数的时间序列,这可能导致气候研究的新研究。