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

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  • Jesús Otero

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  • Jeremy Smith

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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. Copyright Springer-Verlag 2012

Suggested Citation

  • Jesús Otero & Jeremy Smith, 2012. "Response surface models for the Leybourne unit root tests and lag order dependence," Computational Statistics, Springer, vol. 27(3), pages 473-486, September.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:473-486 DOI: 10.1007/s00180-011-0268-y
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    References listed on IDEAS

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    1. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of a Modified Dickey-Fuller Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(3), pages 411-419, August.
    2. Leybourne, S J, 1995. "Testing for Unit Roots Using Forward and Reverse Dickey-Fuller Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(4), pages 559-571, November.
    3. Harvey, David I. & van Dijk, Dick, 2006. "Sample size, lag order and critical values of seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2734-2751, June.
    4. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 277-280, July.
    5. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, pages 1-27.
    6. L. Vanessa Smith & Stephen Leybourne & Tae-Hwan Kim & Paul Newbold, 2004. "More powerful panel data unit root tests with an application to mean reversion in real exchange rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 147-170.
    7. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    8. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    9. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    10. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
    11. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-470, October.
    12. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
    13. Stephen Leybourne & A. M. Robert Taylor, 2003. "Seasonal Unit Root Tests Based on Forward and Reverse Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 441-460, July.
    14. Stephen Leybourne & Tae-Hwan Kim & Paul Newbold, 2005. "Examination of Some More Powerful Modifications of the Dickey-Fuller Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 355-369, May.
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    Citations

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    Cited by:

    1. Hector M. Nuñez and Jesús Otero, 2017. "Integration in Gasoline and Ethanol Markets in Brazil over Time and Space under the Flex-fuel Technology," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    2. Mark J. Holmes & Jesús Otero & Theodore Panagiotidis, 2016. "Climbing the property ladder: An analysis of market integration in London property prices," Working Paper series 16-30, Rimini Centre for Economic Analysis.
    3. Holmes, Mark J. & Iregui, Ana María & Otero, Jesús, 2015. "Interest rate pass through and asymmetries in retail deposit and lending rates: An analysis using data from Colombian banks," Economic Modelling, Elsevier, vol. 49(C), pages 270-277.
    4. Mark J. Holmes & Jesús Otero & Theodore Panagiotidis, 2017. "A Pair-wise Analysis of Intra-city Price Convergence Within the Paris Housing Market," The Journal of Real Estate Finance and Economics, Springer, vol. 54(1), pages 1-16, January.
    5. Holmes, Mark J. & Otero, Jesús & Panagiotidis, Theodore, 2015. "The expectations hypothesis and decoupling of short- and long-term US interest rates: A pairwise approach," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 301-313.
    6. Richard T. Baillie & Kun Ho Kim, 2015. "Local Deviations from Uncovered Interest Parity: The Role of Macroeconomic Fundamentals," Working Paper series 15-43, Rimini Centre for Economic Analysis.
    7. repec:eee:eneeco:v:63:y:2017:i:c:p:314-321 is not listed on IDEAS

    More about this item

    Keywords

    Monte Carlo; Critical values; Lag length; p-values; C12; C15;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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