A test of linearity against functional-coefficient autoregressive models

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Our object in this paper is to propose a powerful test for detecting a broad class of nonlinearity of time series as one application of the method by Matsuda (1998). Consider autoregressive models Xt = φ1Xt-1 + ⋯ + φpXt-p + εt and we propose a statistic for testing whether or not φi depends on delayed values Xt-d for some i. We compare the power of our test with that of tests proposed by Luukkonen, Saikkonen and Teräsvirta (1988a) and Hjellvik and Tjøstheim (1995) by simulation studies and our test is shown to be satisfactory.

Original languageEnglish
Pages (from-to)2539-2551
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Issue number11
Publication statusPublished - 1999


  • Autoregressive models
  • Nonlinear time series
  • Ordinary least squares estimator
  • Weighted least squares estimator


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