Testing a linear time series model against its threshold extension

Guodong LI, Wai Keung LI

Research output: Contribution to journalArticlespeer-review

28 Citations (Scopus)


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 Biometrika Trust.
Original languageEnglish
Pages (from-to)243-250
Issue number1
Publication statusPublished - Mar 2011


Li, G., & Li, W. K. (2011). Testing a linear time series model against its threshold extension. Biometrika, 98(1), 243-250. doi: 10.1093/biomet/asq074


  • Autoregressive moving average model
  • Bootstrap method
  • Quasilikelihood ratio test
  • Threshold model


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