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LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power

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  • Serena Ng
  • Pierre Perron

Abstract

It is widely known that when there are errors with a moving-average root close to - 1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the "AIC" and the "BIC" tend to select a truncation lag ("k") that is very small. We consider a class of Modified Information Criteria ("MIC") with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on "k" and adapts to the type of deterministic components present. We use a local asymptotic framework in which the moving-average root is local to - 1 to document how the "MIC" performs better in selecting appropriate values of "k". In Monte-Carlo experiments, the "MIC" is found to yield huge size improvements to the "DF-super-GLS" and the feasible point optimal "P-sub-T" test developed in Elliott, Rothenberg, and Stock (1996). We also extend the "M" tests developed in Perron and Ng (1996) to allow for "GLS" detrending of the data. The "MIC" along with "GLS" detrended data yield a set of tests with desirable size and power properties. Copyright The Econometric Society.

Suggested Citation

  • Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  • Handle: RePEc:ecm:emetrp:v:69:y:2001:i:6:p:1519-1554
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    References listed on IDEAS

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    1. 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.
    2. Serena Ng & Pierre Perron, 2005. "A Note on the Selection of Time Series Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 115-134, February.
    3. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
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    6. Dufour, J-M. & King, M.L., 1989. "Optimal Invariant Tests For The Autocorrelation Coefficient In Linear Regressions With Stationary And Nonstationary Ar(1) Errors," Cahiers de recherche 8921, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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    12. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Universite de Montreal, Departement de sciences economiques.
    13. Lopez, J. Humberto, 1997. "The power of the ADF test," Economics Letters, Elsevier, vol. 57(1), pages 5-10, November.
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    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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