Testing for Threshold Effects in the TARMA Framework

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 various forms of model mis-specification and have a performance that is not affected by the unknown order of the model. The tests have low computational burden and do not suffer from some of the drawbacks that affect the quasi-likelihood ratio setting. Lastly, we present an application to a time series of standardized tree-ring growth indexes, and the results can lead to new research in climate studies.