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Statistica Sinica 33 (2023), 1879-1901


Greta Goracci1,6 , Simone Giannerini1 , Kung-Sik Chan2 and Howell Tong3,4,5

1 University of Bologna, 2 University of Iowa, 3 University of Electronic Science
and Technology of China, 4 Tsinghua University, 5 London School
of Economics and Political Science and 6 Free University of Bozen/Bolzano

Abstract: We present supremum Lagrange multiplier tests for comparing a linear ARMA specification against its threshold ARMA extension. We derive the asymptotic distribution of the test statistics under both the null hypothesis and contiguous local alternatives, and prove the consistency of the tests. A Monte Carlo study shows that the tests enjoy good finite-sample properties and are robust against various forms of model mis-specification. Furthermore, the performance of the tests is not affected by the unknown order of the model. The tests have a 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 indices. Our results can lead to new research in climate studies.

Keywords: Lagrange multiplier test, linearity testing, marked empirical processes, threshold ARMA models, tree-rings.

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