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The power of unit root tests against nonlinear local alternatives

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  • Matei Demetrescu
  • Robinson Kruse

Abstract

This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specifically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason for such behavior is the interplay of nonstationarity and nonlinearity. In particular, we show that nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the "amount of nonlinearity"), rendering the linear test more powerful than the nonlinear one. Should however the error variance be small, the nonlinear test has better power against local alternatives. We illustrate this in an asymptotic framework of what we call persistent nonlinearity. The theoretical findings of this article explain previous results in the literature obtained by simulation. Furthermore, our own simulation results suggest that the user-specified adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear) alternatives.
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  • Matei Demetrescu & Robinson Kruse, 2013. "The power of unit root tests against nonlinear local alternatives," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 40-61, January.
    • Handle: RePEc:bla:jtsera:v:34:y:2013:i:1:p:40-61
    DOI: j.1467-9892.2012.00812.x
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    File URL: http://hdl.handle.net/10.1111/j.1467-9892.2012.00812.x
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    Cited by:

    1. Takashi Matsuki, 2016. "Linear and nonlinear comovement in Southeast Asian local currency bond markets: a stepwise multiple testing approach," Empirical Economics, Springer, vol. 51(2), pages 591-619, September.
    2. Ahmad Jafari Samimi & Saeed Karimi Petanlar & Jalal Montazeri Shoorekchali, 2017. "Testing Fiscal Reaction Function in Iran:AnApplication of Nonlinear Dickey-Fuller (NDF) Test," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 21(3), pages 567-581, Summer.
    3. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    4. Harvey David I. & Leybourne Stephen J. & Whitehouse Emily J., 2018. "Testing for a unit root against ESTAR stationarity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-29, February.
    5. Neil Kellard & Denise Osborn & Jerry Coakley & Christian Conrad & Menelaos Karanasos, 2015. "On the Transmission of Memory in Garch-in-Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 706-720, September.
    6. Aaron D. Smallwood, 2016. "A Monte Carlo Investigation of Unit Root Tests and Long Memory in Detecting Mean Reversion in I(0) Regime Switching, Structural Break, and Nonlinear Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 986-1012, June.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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