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Response surface models for the Leybourne unit root tests and lag order dependence

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Abstract

This paper calculates response surface models for a large range of quantiles of the Leybourne (Oxf Bull Econ Stat 57:559–571, 1995) test for the null hypothesis of a unit root against the alternative of (trend) stationarity. The response surface models allow the estimation of critical values for different combinations of number of observations, T, and lag order in the test regressions, p, where the latter can be either specified by the user or optimally selected using a data-dependent procedure. The results indicate that the critical values depend on the method used to select the number of lags. An Excel spreadsheet is available to calculate the p-value associated with a test statistic.

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References

  • Cheung Y-W, Lai KS (1995) Lag order and critical values of the augmented Dickey-Fuller test. J Bus Econ Stat 13: 277–280

    Google Scholar 

  • Cheung Y-W, Lai KS (1995) Lag order and critical values of a modified Dickey and Fuller test. Oxf Bull Econ Stat 57: 411–419

    Article  Google Scholar 

  • DeJong DN, Nankervis JC, Savin NE, Whiteman CH (1992) The power problems of unit root tests in time series with autoregressive errors. J Econom 53: 323–343

    Article  MathSciNet  Google Scholar 

  • Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431

    MathSciNet  MATH  Google Scholar 

  • Elliot G, Rothenberg TJ, Stock JH (1996) Efficient tests for an autoregressive unit root. Econometrica 64: 813–836

    Article  MathSciNet  Google Scholar 

  • Hall A (1994) Testing for a unit root in time series with pretest data-based model selection. J Bus Econ Stat 12: 461–470

    Google Scholar 

  • Harvey DI, van Dijk D (2006) Sample size, lag order and critical values of seasonal unit root tests. Comput Stat Data Anal 50: 2734–2751

    Article  MATH  Google Scholar 

  • Hylleberg S, Engle RF, Granger CWJ, Yoo BS (1990) Seasonal integration and cointegration. J Econom 44: 215–238

    Article  MathSciNet  MATH  Google Scholar 

  • Leybourne S (1995) Testing for unit roots using forward and reverse Dickey-Fuller regressions. Oxf Bull Econ Stat 57: 559–571

    Article  Google Scholar 

  • Leybourne S, Kim T-H, Newbold P (2005) Examination of some more powerful modifications of the Dickey-Fuller test. J Time Ser Anal 26: 355–369

    Article  MathSciNet  MATH  Google Scholar 

  • Leybourne S, Taylor AMR (2003) Seasonal unit root tests based on forward and reverse estimation. J Time Ser Anal 24: 441–460

    Article  MathSciNet  MATH  Google Scholar 

  • MacKinnon JG (1991) Critical values for cointegration tests. In: Engle RF, Granger CWJ (eds) Long-run economic relationships: readings in cointegration. Oxford University Press, Oxford, pp 267–276

    Google Scholar 

  • Mackinnon JG (1994) Approximate asymptotic distribution functions for unit-root and cointegration tests. J Bus Econ Stat 12: 167–176

    MathSciNet  Google Scholar 

  • Mackinnon JG (1996) Numerical distribution functions for unit root and cointegration tests. J Appl Econom 11: 601–618

    Article  Google Scholar 

  • Ng S, Perron P (1995) Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. J Am Stat Assoc 90: 268–281

    Article  MathSciNet  MATH  Google Scholar 

  • Park HJ, Fuller WA (1995) Alternative estimators and unit root tests for the autoregressive process. J Time Ser Anal 16: 415–429

    Article  MathSciNet  MATH  Google Scholar 

  • Perron P, Ng S (1996) Useful modifications to some unit root tests with dependent errors and their local asymptotic properties. Rev Econ Stud 63: 435–465

    Article  MATH  Google Scholar 

  • Pesaran MH (2007) A simple panel unit root test in the presence of cross section dependence. J Appl Econom 22: 265–312

    Article  MathSciNet  Google Scholar 

  • Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75: 335–346

    Article  MathSciNet  MATH  Google Scholar 

  • Smith LV, Leybourne S, Kim T-H, Newbold P (2004) More powerful panel data unit root tests with an application to mean reversion in real exchange rates. J Appl Econom 19: 147–170

    Article  Google Scholar 

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Authors and Affiliations

  1. Facultad de Economía, Universidad del Rosario, Bogotá, Colombia

    Jesús Otero

  2. Department of Economics, University of Warwick, Coventry, United Kingdom

    Jeremy Smith

Authors
  1. Jesús Otero
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  2. Jeremy Smith
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Correspondence to Jesús Otero.

Additional information

Work on this paper began while Jesús Otero was a Visiting Fellow in the Department of Economics at the University of Warwick. We would like to thank Jürgen Symanzik (Co-editor), an Associate Editor and two anonymous referees for their constructive comments and suggestions that helped to improve our paper. The usual disclaimer applies.

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Otero, J., Smith, J. Response surface models for the Leybourne unit root tests and lag order dependence. Comput Stat 27, 473–486 (2012). https://doi.org/10.1007/s00180-011-0268-y

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  • DOI: https://doi.org/10.1007/s00180-011-0268-y

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