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Chi-square Tests for Parameter Stability

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Author Info
Marine Carrasco () (University of Rochester)

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Abstract

Testing when a nuisance parameter is identified only under the alternative is problematic because the Likelihood Ratio test converges to a nonstandard distribution that may depend on unknown parameters. Examples include testing parameter stability in Structural Change and Threshold models. Our article proposes a class of tests that have the advantage of having a standard distribution, namely a chi-square. In this class, we focus mostly on a Lagrange Multiplier test in an auxiliary regression. We derive the asymptotic power of this test against alternatives which differ from the implicit alternative of the test. We show that this test can be used as a diagonistic test for parameter stability. A Monte Carlo study compares the performance of our tests with other frequently used tests and shows that they have a similar power.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_508.pdf
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Publisher Info
Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 508.

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Length: 28 pages
Date of creation: Sep 2004
Date of revision:
Handle: RePEc:roc:rocher:508

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Postal: UNIVERSITY OF ROCHESTER, CENTER FOR ECONOMIC RESEARCH, DEPARTMENT OF ECONOMICS, HARKNESS 231 ROCHESTER NEW YORK 14627 U.S.A.

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Related research
Keywords: Admissibility smooth transition structural change test Threshold autoregressive models.

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!] (restricted)
    Other versions:
  3. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November. [Downloadable!] (restricted)
  4. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-29, November. [Downloadable!] (restricted)
    Other versions:
  5. CARRASCO, Marine & FLORENS, Jean-Pierre, 2002. "Efficient GMM Estimation Using the Empirical Characteristic Function," IDEI Working Papers 140, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
  6. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March. [Downloadable!] (restricted)
    Other versions:
  7. Diebold, Francis X. & Chen, Celia, 1996. "Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures," Journal of Econometrics, Elsevier, vol. 70(1), pages 221-241, January. [Downloadable!] (restricted)
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  8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March. [Downloadable!] (restricted)
  9. Szroeter, Jerzy, 1978. "A Class of Parametric Tests for Heteroscedasticity in Linear Econometric Models X1-ab," Econometrica, Econometric Society, vol. 46(6), pages 1311-27, November. [Downloadable!] (restricted)
  10. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  11. 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. [Downloadable!] (restricted)
    Other versions:
  12. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July. [Downloadable!] (restricted)
    Other versions:
  13. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December. [Downloadable!]
  14. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October. [Downloadable!] (restricted)
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    Other versions:
  17. Forchini, G., 2002. "Optimal Similar Tests For Structural Change For The Linear Regression Model," Econometric Theory, Cambridge University Press, vol. 18(04), pages 853-867, May. [Downloadable!]
  18. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May. [Downloadable!] (restricted)
  19. Filippo Altissimo & Valentina Corradi, 2002. "Bounds for inference with nuisance parameters present only under the alternative," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 494-519, 06. [Downloadable!] (restricted)
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  20. Carrasco, Marine, 2002. "Misspecified Structural Change, Threshold, and Markov-switching models," Journal of Econometrics, Elsevier, vol. 109(2), pages 239-273, August. [Downloadable!] (restricted)
  21. Marine Carrasco & Mikhail Chernov & Jean-Pierre Florens & Eric Ghysels, 2003. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," CIRANO Working Papers 2003s-02, CIRANO. [Downloadable!]
    Other versions:
  22. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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