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Hybrid bootstrap aided unit root testing

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Abstract

In this paper, we propose a hybrid bootstrap procedure for augmented Dickey-Fuller (ADF) tests for the presence of a unit root. This hybrid proposal combines a time domain parametric autoregressive fit to the data and a nonparametric correction applied in the frequency domain to capture features that are possibly not represented by the parametric model. It is known that considerable size and power problems can occur in small samples for unit root testing in the presence of an MA parameter using critical values of the asymptotic Dickey-Fuller distribution. The benefit of the sieve bootstrap in this situation has been investigated by Chang and Park (J Time Ser Anal 24:379–400, 2003). They showed asymptotic validity as well as substantial improvements for small sample sizes, but the actual sizes of their bootstrap tests were still quite far away from the nominal size. The finite sample performances of our procedure are extensively investigated through Monte Carlo simulations and compared to the sieve bootstrap approach. Regarding the size of the tests, our results show that the hybrid bootstrap remarkably outperforms the sieve bootstrap.

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Authors and Affiliations

  1. Department of Economics, University of Mannheim, L7, 3-5, 68131, Mannheim, Germany

    C. Jentsch

  2. Institut für Mathematische Stochastik, Technische Universität Braunschweig, Pockelsstraße 14, 38106, Braunschweig, Germany

    J.-P. Kreiss

  3. Department of Statistics, Swedish Business School, University of Örebro, 701 82, Örebro, Sweden

    P. Mantalos

  4. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    E. Paparoditis

Authors
  1. C. Jentsch
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  2. J.-P. Kreiss
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  3. P. Mantalos
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  4. E. Paparoditis
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Corresponding author

Correspondence to P. Mantalos.

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Jentsch, C., Kreiss, JP., Mantalos, P. et al. Hybrid bootstrap aided unit root testing. Comput Stat 27, 779–797 (2012). https://doi.org/10.1007/s00180-011-0290-0

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  • DOI: https://doi.org/10.1007/s00180-011-0290-0

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