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Comment on: Threshold Autoregressions With a Unit Root


  • Jean-Yves Pitarakis


In this paper we revisit the results in Caner and Hansen (2001), where the authors obtained novel limiting distributions of Wald type test statistics for testing for the presence of threshold nonlinearities in autoregressive models containing unit roots. Using the same framework, we obtain a new formulation of the limiting distribution of the Wald statistic for testing for threshold effects, correcting an expression that appeared in the main theorem presented by Caner and Hansen. Subsequently, we show that under a particular scenario that excludes stationary regressors such as lagged dependent variables and despite the presence of a unit root, this same limiting random variable takes a familiar form that is free of nuisance parameters and already tabulated in the literature, thus removing the need to use bootstrap based inferences. This is a novel and unusual occurrence in this literature on testing for the presence of nonlinear dynamics. Copyright 2008 The Econometric Society.

Suggested Citation

  • Jean-Yves Pitarakis, 2008. "Comment on: Threshold Autoregressions With a Unit Root," Econometrica, Econometric Society, vol. 76(5), pages 1207-1217, September.
  • Handle: RePEc:ecm:emetrp:v:76:y:2008:i:5:p:1207-1217

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    Cited by:

    1. Mehmet Caner & Thomas Grennes, 2010. "Sovereign Wealth Funds: The Norwegian Experience," The World Economy, Wiley Blackwell, vol. 33(4), pages 597-614, April.
    2. Jesús Gonzalo & Jean-Yves Pitarakis, 2013. "Estimation and inference in threshold type regime switching models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 8, pages 189-205 Edward Elgar Publishing.
    3. Christopoulos, Dimitris & McAdam, Peter & Tzavalis, Elias, 2018. "Dealing with endogeneity in threshold models using copulas: an illustration to the foreign trade multiplier," Working Paper Series 2136, European Central Bank.
    4. repec:taf:jnlbes:v:35:y:2017:i:2:p:202-217 is not listed on IDEAS
    5. Jesùs Gonzalo & Jean-Yves Pitarakis, 2017. "Inferring the Predictability Induced by a Persistent Regressor in a Predictive Threshold Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 202-217, April.
    6. Pitarakis, Jean-Yves, 2012. "Jointly testing linearity and nonstationarity within threshold autoregressions," Economics Letters, Elsevier, vol. 117(2), pages 411-413.

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