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Constructing Optimal Tests on a Lagged Dependent Variable

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  • Patrick Marsh
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    Abstract

    Via the leading unit root case, the problem of testing on a lagged dependent variable is characterized by a nuisance parameter which is present only under the alternative (see Andrews and Ploberger (1994)). This has proven a barrier to the construction of optimal tests. Moreover, in their absence it is impossible to objectively assess the absolute power properties of existing tests. Indeed, feasible tests based upon the optimality criteria used here are found to have numerically superior power properties to both the original Dickey and Fuller (1981) statistics and the efficient detrended versions suggested by Elliott, Rothenberg and Stock (1996) and analysed in Burridge and Taylor (2000).

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    Bibliographic Info

    Paper provided by Department of Economics, University of York in its series Discussion Papers with number 06/19.

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    Date of creation: Oct 2006
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    Handle: RePEc:yor:yorken:06/19

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    Keywords: Nuisance parameter; invariant test; unit root;

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    1. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
    2. 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.
    3. Hillier, Grant H., 1987. "Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems," Econometric Theory, Cambridge University Press, vol. 3(01), pages 1-44, February.
    4. Giovanni Forchini & Patrick Marsh, . "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York.
    5. Burridge, Peter & Taylor, A M Robert, 2000. " On the Power of GLS-Type Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(5), pages 633-45, December.
    6. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
    7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    8. Forchini, Giovanni, 2005. "Optimal weighted average power similar tests for the covariance structure in the linear regression model," Journal of Econometrics, Elsevier, vol. 124(2), pages 253-267, February.
    9. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
    10. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
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