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Testing for Threshold Effects in the TARMA Framework
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Testing for Threshold Effects in the TARMA Framework

Greta Goracci, Simone Giannerini, Kung-Sik Chan and Howell Tong
ArXiv.org
Cornell University
03/25/2021
DOI: 10.48550/arxiv.2103.13977
url
https://doi.org/10.5705/ss.202021.0120View
Published (Version of record)This article has now been published in a journal and has been peer-reviewed by subject experts. This version may differ significantly from the preprint version. Restricted
url
https://doi.org/10.48550/arxiv.2103.13977View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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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 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.
 Mathematics - Statistics Theory Methodology (stat.ME) Statistics Theory (math.ST) FOS: Mathematics Economics - Econometrics Lagrange multiplier test Linearity testing Statistics, Probability and Uncertainty Statistics - Methodology Marked empirical processe Threshold autoregressive moving-average model FOS: Computer and information sciences Econometrics (econ.EM) 62M10, 91B84 FOS: Economics and business Statistics and Probability tree-rings

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