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

  • Serena Ng
  • Pierre Perron

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.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 69 (2001)
Issue (Month): 6 (November)
Pages: 1519-1554

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Handle: RePEc:ecm:emetrp:v:69:y:2001:i:6:p:1519-1554
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  1. Serena Ng & Pierre Perron, 2001. "A Note on the Selection of Time Series Models," Boston College Working Papers in Economics 500, Boston College Department of Economics.
  2. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  3. Nabeya, S. & Perron, P., 1991. "Local Asymtotic Distributions Related to the AR(1) MOdel with Dependent Errors," Papers 362, Princeton, Department of Economics - Econometric Research Program.
  4. 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.
  5. 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.
  6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  7. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  8. 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, Universite de Montreal, Departement de sciences economiques.
  9. Perron, Pierre & Ng, Serena, 1998. "An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 14(05), pages 560-603, October.
  10. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Universite de Montreal, Departement de sciences economiques.
  11. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
  12. Franses, Philip Hans & Haldrup, Niels, 1994. "The Effects of Additive Outliers on Tests for Unit Roots and Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 471-78, October.
  13. Lopez, J. Humberto, 1997. "The power of the ADF test," Economics Letters, Elsevier, vol. 57(1), pages 5-10, November.
  14. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
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