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Testing for Linearity in Regressions with I(1) Processes

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  • Yoichi Arai

    (National Graduate Institute for Policy Studies)

Abstract
We propose a generalized version of the RESET test for linearity in regressions with I(1) processes against various nonlinear alternatives and no cointegration. The proposed test statistic for linearity is given by the Wald statistic and its limiting distribution under the null hypothesis is shown to be a X^2 distribution with a "leads and lags" estimation technique. We show that the test is consistent against a class of nonlinear alternatives and no cointegration. Finite-sample simulations show that the empirical size is close to the nominal one and the test succeeds in detecting both nonlinearity and no cointegration.

Suggested Citation

  • Yoichi Arai, 2015. "Testing for Linearity in Regressions with I(1) Processes," GRIPS Discussion Papers 15-11, National Graduate Institute for Policy Studies.
    • Handle: RePEc:ngi:dpaper:15-11
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    Cited by:

    1. Yoichi Arai & Eiji Kurozumi, 2007. "Testing for the Null Hypothesis of Cointegration with a Structural Break," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 705-739.
    2. Chang, Chun-Ping & Lee, Chien-Chiang & Hsieh, Meng-Chi, 2015. "Does globalization promote real output? Evidence from quantile cointegration regression," Economic Modelling, Elsevier, vol. 44(C), pages 25-36.
    3. Rickard Sandberg, 2017. "Sample Moments and Weak Convergence to Multivariate Stochastic Power Integrals," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1000-1009, November.
    4. Christopoulos, Dimitris & León-Ledesma, Miguel A., 2010. "Current account sustainability in the US: What did we really know about it?," Journal of International Money and Finance, Elsevier, vol. 29(3), pages 442-459, April.
    5. Abm Nasir & Abdullah M. Noman, 2012. "Sustainability of external debt: further evidence from non-linear framework," International Review of Applied Economics, Taylor & Francis Journals, vol. 26(5), pages 673-685, December.
    6. Yoichi Arai & Eiji Kurozumi, 2005. "Testing for the Null Hypothesis of Cointegration with Structural Breaks (Subsequently published in "Econometric Reviews", Volume 26, Issue 6 November 2007, pages 705 - 739. )," CARF F-Series CARF-F-022, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Gonzalo, Jesùs & Pitarakis, Jean-Yves, 2005. "Threshold effects In multivariate error correction models," Discussion Paper Series In Economics And Econometrics 0501, Economics Division, School of Social Sciences, University of Southampton.
    8. Seo Byeongseon, 2011. "Nonparametric Testing for Linearity in Cointegrated Error-Correction Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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