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Structural Stability Tests with Unknown Breakpoint for the Efficient Method of Moments with Application to Stochastic Volatility Models

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  • Pieter J. van der Sluis

    (University of Amsterdam)

Abstract

Tests for structural stability with unknown breakpoint are derived for and applied tothe efficient method of moments. Three types of tests are discerned: Wald type tests,Predictive tests and Hansen type tests. The Hansen type test for structural stabilitywith unknown breakpoint is a novelty for moment based techniques. Therefore for thistest asymptotic and local power results are provided. It turns out this test has thesame asymptotic distribution as the Hall and Sen test. All these tests are applied toan asymmetric stochastic volatility model for a series of daily observations of theS&P 500 index over the years 1963-1993. Our results indicate that the asymmetricstochastic volatility models fails all stability tests. The supremum type tests givean estimate of the breakpoint in first half of 1970. However the model seems to becomemore stable as time proceeds.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 98-055/4.

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Date of creation: 20 May 1998
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Handle: RePEc:dgr:uvatin:19980055

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  1. Sowell, Fallaw, 1996. "Optimal Tests for Parameter Instability in the Generalized Method of Moments Framework," Econometrica, Econometric Society, Econometric Society, vol. 64(5), pages 1085-1107, September.
  2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 821-56, July.
  3. Tauchen, George & Zhang, Harold & Liu, Ming, 1996. "Volume, volatility, and leverage: A dynamic analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 177-208, September.
  4. Ghysels, E & Hall, A., 1988. "A Test For Structural Stability Of Euler Conditions Parameters Estimated Via The Generalized Methods Of Moments Estimators," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 8837, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Ghysels, Eric & Hall, Alastair, 1990. "Are consumption-based intertemporal capital asset pricing models structural?," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 121-139.
  6. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers, CIRANO 95s-49, CIRANO.
  7. Eric Ghysels & Alain Guay & Alastair Hall, 1995. "Predictive Tests for Structural Change with Unknown Breakpoint," CIRANO Working Papers, CIRANO 95s-20, CIRANO.
  8. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers, Toulouse - GREMAQ 92.279, Toulouse - GREMAQ.
  9. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers, Duke University, Department of Economics 95-20, Duke University, Department of Economics.
  10. Andrews, Donald W. K. & Lee, Inpyo & Ploberger, Werner, 1996. "Optimal changepoint tests for normal linear regression," Journal of Econometrics, Elsevier, Elsevier, vol. 70(1), pages 9-38, January.
  11. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1015, Cowles Foundation for Research in Economics, Yale University.
  12. Fallaw Sowell, . "Tests for Violations of Moment Conditions," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 21, Carnegie Mellon University, Tepper School of Business.
  13. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 363-90, March.
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  15. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  16. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, Elsevier, vol. 77(2), pages 343-377, April.
  17. Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers, Duke University, Department of Economics 96-17, Duke University, Department of Economics.
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  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  20. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(4), pages 429-34, October.
  21. Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
  22. Bansal, Ravi & Gallant, A. Ronald & Hussey, Robert & Tauchen, George, 1995. "Nonparametric estimation of structural models for high-frequency currency market data," Journal of Econometrics, Elsevier, Elsevier, vol. 66(1-2), pages 251-287.
  23. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
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  25. Hall, Alastair R & Sen, Amit, 1999. "Structural Stability Testing in Models Estimated by Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 17(3), pages 335-48, July.
  26. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, Elsevier, vol. 29(3), pages 229-256, September.
  27. Pieter J. Van Der Sluis, 1998. "Computationally attractive stability tests for the efficient method of moments," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C203-C227.
  28. Hoffman, Dennis L & Pagan, Adrian R, 1989. "Post-Sample Prediction Tests for Generalized Method of Moments Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 51(3), pages 333-43, August.
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Cited by:
  1. Eric Ghysels & Alain Guay, 2001. "Testing for Structural Change in the Presence of Auxiliary Models," Cahiers de recherche CREFE / CREFE Working Papers, CREFE, Université du Québec à Montréal 133, CREFE, Université du Québec à Montréal.

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