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Weighted Average Power Similar Tests for Structural Change for the Gaussian Linear Regression Model

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  • Giovanni Forchini

Abstract

The average exponential tests for structural change of Andrews and Ploberger (Econometrica, 62, 1994) and Andrews, Lee and Ploberger (Journal of Econometrics 70, 1996) and modifications thereof maximize a weighted average power which incorporates specific weighting functions in order to make the resulting test statistics simple. Generalizations of these tests involve the numerical evaluation of (potentially) complicated integrals. In this paper we suggest a uniform Laplace approximation to evaluate weighted average power test statistics for which a simple closed form does not exist. We also show that a modification of the avg-F test is optimal under a very large class of weighting functions and can be written as a ratio of quadratic forms. Finally, we discuss how the computational burden of averaging over all possible change-points can be addressed.

Suggested Citation

  • Giovanni Forchini, 2005. "Weighted Average Power Similar Tests for Structural Change for the Gaussian Linear Regression Model," Monash Econometrics and Business Statistics Working Papers 20/05, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2005-20
    as

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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp20-05.pdf
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    References listed on IDEAS

    as
    1. Forchini, G., 2002. "Optimal Similar Tests For Structural Change For The Linear Regression Model," Econometric Theory, Cambridge University Press, vol. 18(4), pages 853-867, August.
    2. 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.
    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(1), pages 1-44, February.
    4. Andrews, Donald W. K. & Lee, Inpyo & Ploberger, Werner, 1996. "Optimal changepoint tests for normal linear regression," Journal of Econometrics, Elsevier, vol. 70(1), pages 9-38, January.
    5. Marine Carrasco, 2004. "Chi-square Tests for Parameter Stability," RCER Working Papers 508, University of Rochester - Center for Economic Research (RCER).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Linear Regression Model; Similar Tests; Invariant Tests; Structural Change; Weighted Average Power Tests; Laplace Approximation; Uniform Laplace Approximation.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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