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Constructing Optimal Tests on a Lagged Dependent Variable

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  • Patrick Marsh

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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  • Patrick Marsh, 2006. "Constructing Optimal Tests on a Lagged Dependent Variable," Discussion Papers 06/19, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:06/19
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    References listed on IDEAS

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    1. Giovanni Forchini & Patrick Marsh, "undated". "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York.
    2. Peter Burridge & A. M. Robert Taylor, 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 633-645, December.
    3. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    4. repec:bla:obuest:v:62:y:2000:i:5:p:633-45 is not listed on IDEAS
    5. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    6. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    7. 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.
    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. 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 1057-1072, June.
    10. Hillier, Grant H., 1987. "Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems," Econometric Theory, Cambridge University Press, vol. 3(1), pages 1-44, February.
    11. 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.
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    Cited by:

    1. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 15/13, Institute for Fiscal Studies.
    2. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    3. Patrick Marsh, 2019. "Properties of the power envelope for tests against both stationary and explosive alternatives: the effect of trends," Discussion Papers 19/03, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Wang Liqiong, 2013. "Bootstrap Point Optimal Unit Root Tests," Journal of Time Series Econometrics, De Gruyter, vol. 6(1), pages 1-31, July.
    5. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 41/13, Institute for Fiscal Studies.

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    Keywords

    Nuisance parameter; invariant test; unit root;
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