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Maximum likelihood and the bootstrap for nonlinear dynamic models

  • Goncalves, Silvia
  • White, Halbert

We provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes. We apply our results to the moving blocks bootstrap of Kunsch (1989) and Liu and Singh (1992) and prove the first order asymptotic validity of the bootstrap approximation to the true distribution of quasi-maximum likelihood estimators. We also consider bootstrap testing. In particular, we prove the first order asymptotic validity of the bootstrap distribution of suitable bootstrap analogs of Wald and Lagrange Multiplier statistics for testing hypotheses.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(03)00204-5
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 119 (2004)
Issue (Month): 1 (March)
Pages: 199-219

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Handle: RePEc:eee:econom:v:119:y:2004:i:1:p:199-219
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2001.
  2. 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.
  3. Goncalves, Silvia & White, Halbert, 2000. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series qt1bj657ff, Department of Economics, UC San Diego.
  4. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
  5. Goncalves, S. & White, H., 2001. "The Bootstrap of Mean for Dependent Heterogeneous Arrays," Cahiers de recherche 2001-19, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. repec:cup:etheor:v:12:y:1996:i:1:p:187-97 is not listed on IDEAS
  7. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Testing in Nonlinear Models," G.R.E.Q.A.M. 97a39, Universite Aix-Marseille III.
  8. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
  9. Atsushi Inoue & Mototsugu Shintani, 2001. "Bootstrapping GMM Estimators for Time Series," Vanderbilt University Department of Economics Working Papers 0129, Vanderbilt University Department of Economics, revised Aug 2003.
  10. Sílvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO.
  11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  12. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics.
  13. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
  14. Hahn, Jinyong, 1996. "A Note on Bootstrapping Generalized Method of Moments Estimators," Econometric Theory, Cambridge University Press, vol. 12(01), pages 187-197, March.
  15. Shao, Jun, 1992. "Bootstrap variance estimators with truncation," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 95-101, September.
  16. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
  17. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  18. Lahiri, Soumendra Nath, 1996. "On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 42-59, January.
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