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A comparison of alternative unit root tests

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  • George Halkos
  • Ilias Kevork

Abstract

In this paper we evaluate the performance of three methods for testing the existence of a unit root in a time series, when the models under consideration in the null hypothesis do not display autocorrelation in the error term. In such cases, simple versions of the Dickey-Fuller test should be used as the most appropriate ones instead of the known augmented Dickey-Fuller or Phillips-Perron tests. Through Monte Carlo simulations we show that, apart from a few cases, testing the existence of a unit root we obtain actual type I error and power very close to their nominal levels. Additionally, when the random walk null hypothesis is true, by gradually increasing the sample size, we observe that p-values for the drift in the unrestricted model fluctuate at low levels with small variance and the Durbin-Watson (DW) statistic is approaching 2 in both the unrestricted and restricted models. If, however, the null hypothesis of a random walk is false, taking a larger sample, the DW statistic in the restricted model starts to deviate from 2 while in the unrestricted model it continues to approach 2. It is also shown that the probability not to reject that the errors are uncorrelated, when they are indeed not correlated, is higher when the DW test is applied at 1% nominal level of significance.

Suggested Citation

  • George Halkos & Ilias Kevork, 2005. "A comparison of alternative unit root tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 45-60.
  • Handle: RePEc:taf:japsta:v:32:y:2005:i:1:p:45-60 DOI: 10.1080/0266476052000330286
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    References listed on IDEAS

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    1. Chao-Yu Chou & Chung-Ho Chen & Hui-Rong Liu, 2000. "Economic-statistical design of X ¥ charts for non-normal data by considering quality loss," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 939-951.
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    Cited by:

    1. Halkos, George & Kevork, Ilias & Galani, Georgia & Tzeremes, Panagiotis, 2014. "An analysis of long-term scenarios for the transition to renewable energy in Greece," MPRA Paper 59975, University Library of Munich, Germany.
    2. George, Halkos & Ilias, Kevork, 2005. "Το Υπόδειγμα Τυχαίου Περιπάτου Με Αυτοπαλίνδρομα Σφάλματα
      [The random walk model with autoregressive errors]
      ," MPRA Paper 33312, University Library of Munich, Germany.
    3. Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "Emissions and abatement costs for the passenger cars sector in Greece," MPRA Paper 60197, University Library of Munich, Germany.
    4. Halkos, George & Kevork, Ilias, 2012. "Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis," MPRA Paper 40724, University Library of Munich, Germany.
    5. Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "Greenhouse gas emissions and marginal abatement cost curves for the road transport in Greece," MPRA Paper 61032, University Library of Munich, Germany.
    6. George, Halkos & Ilias, Kevork, 2004. "H Ασυμπτωτική Διακύμανση Στην Εκτίμηση Του Στάσιμου Μέσου Υπό Συνθήκες Αυτοσυσχέτισης
      [Using the asymptotic variance to estimate the stationary mean under autocorrelation]
      ," MPRA Paper 33324, University Library of Munich, Germany.

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