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Testing for threshold effects in the TARMA framework

Author

Listed:
  • Greta Goracci
  • Simone Giannerini
  • Kung-Sik Chan
  • Howell Tong

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.

Suggested Citation

  • Greta Goracci & Simone Giannerini & Kung-Sik Chan & Howell Tong, 2021. "Testing for threshold effects in the TARMA framework," Papers 2103.13977, arXiv.org.
    • Handle: RePEc:arx:papers:2103.13977
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    File URL: http://arxiv.org/pdf/2103.13977
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    References listed on IDEAS

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    1. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    2. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
    3. Simone Giannerini & Esfandiar Maasoumi & Estela Bee Dagum, 2015. "Entropy testing for nonlinear serial dependence in time series," Biometrika, Biometrika Trust, vol. 102(3), pages 661-675.
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    Cited by:

    1. Francesco Angelini & Massimiliano Castellani & Simone Giannerini & Greta Goracci, 2025. "Testing for Threshold Effects in the Presence of Heteroskedasticity and Measurement Error With an Application to Italian Strikes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 87(3), pages 659-689, June.
    2. Heiko Rachinger & Edward M. H. Lin & Henghsiu Tsai, 2024. "A bootstrap test for threshold effects in a diffusion process," Computational Statistics, Springer, vol. 39(5), pages 2859-2872, July.
    3. Ahmed Ghezal & Maddalena Cavicchioli & Imane Zemmouri, 2024. "On the existence of stationary threshold bilinear processes," Statistical Papers, Springer, vol. 65(6), pages 3739-3767, August.

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