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Testing a linear time series model against its threshold extension

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  • Guodong Li
  • Wai Keung Li

Abstract

This paper derives the asymptotic null distribution of a quasilikelihood ratio test statistic for an autoregressive moving average model against its threshold extension. The null hypothesis is that of no threshold, and the error term could be dependent. The asymptotic distribution is rather complicated, and all existing methods for approximating a distribution in the related literature fail to work. Hence, a novel bootstrap approximation based on stochastic permutation is proposed in this paper. Besides being robust to the assumptions on the error term, our method enjoys more flexibility and needs less computation when compared with methods currently used in the literature. Monte Carlo experiments give further support to the new approach, and an illustration is reported. Copyright 2011, Oxford University Press.

Suggested Citation

  • Guodong Li & Wai Keung Li, 2011. "Testing a linear time series model against its threshold extension," Biometrika, Biometrika Trust, vol. 98(1), pages 243-250.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:243-250
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    File URL: http://hdl.handle.net/10.1093/biomet/asq074
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    Cited by:

    1. Hui, Yongchang & Wong, Wing-Keung & Bai, Zhidong & Zhu, Zhenzhen, 2016. "A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications," MPRA Paper 75216, University Library of Munich, Germany.
    2. Giannerini, Simone & Goracci, Greta & Rahbek, Anders, 2024. "The validity of bootstrap testing for threshold autoregression," Journal of Econometrics, Elsevier, vol. 239(1).

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