Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T23:11:34.329Z Has data issue: false hasContentIssue false
  • English
  • Français

A Nonparametric Conditional Moment Test for Structural Stability

Published online by Cambridge University Press:  11 February 2009

Javier Hidalgo
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a nonparametric conditional moment test of stability of an econometric model against the alternative of instability. The alternative hypothesis allows for more than one structural change, although in this case it has to be fairly smooth. This complements existing results for stability in a parametric setting. Also, it is shown that the test is always consistent, unlike the available “parametric” tests, which normally rely on the assumption of a correct specification of the model, at least under the null hypothesis of no structural instability. Moreover, we show that the test has local power comparable to the parametric ones; that is, its asymptotic efficiency is greater than zero. A Monte Carlo experiment about the performance of our test is described.

Type
Research Article
Information
Econometric Theory , Volume 11 , Issue 4 , August 1995 , pp. 671 - 698
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1993) Test for parameter instability and structural change with unknown change point. Econometrica 61, 821–856.10.2307/2951764CrossRefGoogle Scholar
Andrews, D.W.K. & Fair, R.C. (1988) Inference in nonlinear econometric models with structural change. Review of Economic Studies 55, 615–640.10.2307/2297408CrossRefGoogle Scholar
Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414.10.2307/2951753CrossRefGoogle Scholar
Bai, J., Lumsdaine, R.L., & Stock, J.H. (1991) Testing for and Dating Breaks in Integrated and Cointegarated Time Series. Preprint, Harvard University.Google Scholar
Bierens, H. (1990) A consistent conditional moment test of functional form. Econometrica 58, 1443–1458.10.2307/2938323CrossRefGoogle Scholar
Brown, R.L., Durbin, J., & Evans, J.M. (1975) Techniques for testing the constancy of regression relationships over time (with discussion). Journal of the Royal Statistical Society, Series B 37, 149–192.Google Scholar
Chow, G.C. (1960) Test of equality between sets of coefficients in two linear regressions. Econometrica 28, 591–605.10.2307/1910133CrossRefGoogle Scholar
Chu, C.J. & White, H. (1992) A direct test for changing trend. Journal of Business and Economic Statistics 10, 289–299.CrossRefGoogle Scholar
Epanechnikov, V.A. (1969) Nonparametric estimators of a multivariate probability density. Theory of Probability and Its Applications 14, 153–158.10.1137/1114019CrossRefGoogle Scholar
Hackl, P. (1989) Statistical Analysis and Forecasting of Economic Structure Change. Berlin: Springer-Verlag.10.1007/978-3-662-02571-0CrossRefGoogle Scholar
Hackl, P. & Westlund, A. (1991) Economic Structural Change, Analysis and Forecasting. Berlin: Springer-Verlag.10.1007/978-3-662-06824-3CrossRefGoogle Scholar
Hansen, B.E. (1990) Lagrange Multiplier Tests for Parameter Instability in Non-linear Models. Preprint, University of Rochester.Google Scholar
Hansen, B.E. (1992) Tests for parameter instability in regressions with I (1) processes. Journal of Business and Economic Statistics 10, 321–335.Google Scholar
Harel, M. & Puri, M.L. (1990) Weak invariance of generalized U-statistics for nonstationary absolute regular processes. Stochastic Processes and Their Applications 34, 341–360.10.1016/0304-4149(90)90022-KCrossRefGoogle Scholar
Hidalgo, J. (1992) Adaptive semiparametric estimation in the presence of autocorrelation of unknown form. Journal of Time Series Analysis 13, 47–78.10.1111/j.1467-9892.1992.tb00094.xCrossRefGoogle Scholar
Kim, H.J. & Siegmund, D. (1989) The likelihood ratio test for a change-point in single linear regression. Biometrika 76, 409–423.10.1093/biomet/76.3.409CrossRefGoogle Scholar
Krämer, W., Ploberger, W., & Alt, R. (1988) Testing for structural change in dynamic models. Econometrica 56, 1355–1369.10.2307/1913102CrossRefGoogle Scholar
Loéve, M. (1977) Probability Theory,.vol. 1, New York: Springer-Verlag.Google Scholar
Newey, W. (1985) Maximum likelihood specification testing and conditional moment test. Econometrica 53, 1047–1070.10.2307/1911011CrossRefGoogle Scholar
Ploberger, W. & Krämer, W. (1992) The CUSUM test with OLS residuals. Econometrica 60, 271–285.10.2307/2951597CrossRefGoogle Scholar
Ploberger, W., Krämer, W., & Kontrus, K. (1989) A new test for structural stability in the linear regression model. Journal of Econometrics 40, 307–318.10.1016/0304-4076(89)90087-0CrossRefGoogle Scholar
Powell, J., Stock, J., & Stoker, T. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1403–1430.10.2307/1913713CrossRefGoogle Scholar
Quandt, R. (1960) Tests of the hypothesis that a linear regression system obeys two separate regimes. Journal of the American Statistical Association 55, 324–330.10.1080/01621459.1960.10482067CrossRefGoogle Scholar
Robinson, P.M. (1988) Root-N-consistency semiparametric regression. Econometrica 56, 931–954.10.2307/1912705CrossRefGoogle Scholar
Robinson, P.M. (1989) Nonparametric estimation of time-varying parameters. In Hackl, P. (ed.), Statistical Analysis and Forecasting of Economic Structural Change, pp. 253–264. Berlin: Springer-Verlag.10.1007/978-3-662-02571-0_15CrossRefGoogle Scholar
Yoshihara, K. (1976) Limiting behaviour of U-statistics for stationary absolutely regular processes. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 35, 237–252.10.1007/BF00532676CrossRefGoogle Scholar