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Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models

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Author Info
Sílvia Gonçalves ()
Halbert White

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Abstract

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 Künsch (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.

Nous proposons une approche unifiée pour analyser la méthode de bootstrap appliquée aux estimateurs de pseudo-maximum de vraisemblance dans le contexte de modèles non linéaires dynamiques où les données sont caractérisées par une dépendance d'époque proche. Nous appliquons nos résultats à la méthode de bootstrap de blocs mouvants de Künsch (1989) et Liu et Singh (1992) et nous démontrons la validité asymptotique de premier ordre de l'approximation du bootstrap à la distribution asymptotique de l'estimateur de pseudo-maximum de vraisemblance. Nous considérons aussi l'application du bootstrap à la réalisation de tests d'hypothèses. En particulier, nous démontrons la validité asymptotique des versions de bootstrap des tests de Wald et du multiplicateur de Lagrange.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-41.

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Date of creation: 01 Apr 2002
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Handle: RePEc:cir:cirwor:2002s-41

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Related research
Keywords: Block bootstrap; quasi-maximum likelihood estimator; nonlinear dynamic model; near epoch dependence; Wald test; Bootstrap en bloc; pseudo-maximum de vraisemblance; modèle non linéaire dynamique; dépendance d'époque proche; test de Wald;

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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. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August. [Downloadable!] (restricted)
    Other versions:
  3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  4. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October. [Downloadable!] (restricted)
  5. Sílvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO. [Downloadable!]
    Other versions:
  6. repec:cup:etheor:v:12:y:1996:i:1:p:187-97 is not listed on IDEAS
  7. Hahn, Jinyong, 1996. "A Note on Bootstrapping Generalized Method of Moments Estimators," Econometric Theory, Cambridge University Press, vol. 12(01), pages 187-197, March. [Downloadable!]
  8. 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)
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  9. 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. [Downloadable!] (restricted)
  10. Benedikt Pötscher & Ingmar Prucha, 1991. "Basic structure of the asymptotic theory in dynamic nonlinear econometric models," Econometric Reviews, Taylor and Francis Journals, vol. 10(3), pages 253-325. [Downloadable!] (restricted)
  11. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    Other versions:
  12. GONÇALVES, Silvia & WHITE, Halbert, 2001. "The Bootstrap of Mean for Dependent Heterogeneous Arrays," Cahiers de recherche 2001-19, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  13. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
    Other versions:
  14. 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)
  15. repec:cup:etheor:v:7:y:1991:i:2:p:213-21 is not listed on IDEAS
  16. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July. [Downloadable!] (restricted)
  17. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June. [Downloadable!]
  18. Shao, Jun, 1992. "Bootstrap variance estimators with truncation," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 95-101, September. [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. Richard G. Anderson & Hailong Qian & Robert H. Rasche, 2006. "Analysis of panel vector error correction models using maximum likelihood, the bootstrap, and canonical-correlation estimators," Working Papers 2006-050, Federal Reserve Bank of St. Louis. [Downloadable!]
  2. Valentina Corradi & Norman Swanson, 2004. "Bootstrap Procedures for Recursive Estimation Schemes With Applications to Forecast Model Selection," Departmental Working Papers 200418, Rutgers University, Department of Economics. [Downloadable!]
  3. Valentina Corradi & Norman R. Swanson, 2003. "Evaluation of Dynamic Stochastic General Equilibrium Models Based on Distributional Comparison of Simulated and Historical Data," Departmental Working Papers 200320, Rutgers University, Department of Economics. [Downloadable!]
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  4. Stan Hurn, 2004. "Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity," Econometric Society 2004 Australasian Meetings 348, Econometric Society. [Downloadable!]
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  5. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics. [Downloadable!]
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  6. Robert F. Engle & Neil Shephard & Kevin Sheppard, 2008. "Fitting vast dimensional time-varying covariance models," Economics Series Working Papers 403, University of Oxford, Department of Economics. [Downloadable!]
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  7. Inoue, Atsushi & Kilian, Lutz, 2005. "How Useful is Bagging in Forecasting Economic Time Series? A Case Study of US CPI Inflation," CEPR Discussion Papers 5304, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  8. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Specification Tests for Diffusion Processes," Departmental Working Papers 200321, Rutgers University, Department of Economics. [Downloadable!]
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  9. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics. [Downloadable!]
  10. Valentina Corradi & Norman Swanson, 2003. "The Block Bootstrap for Parameter Estimation Error In Recursive Estimation Schemes, With Applications to Predictive Evaluation," Departmental Working Papers 200313, Rutgers University, Department of Economics. [Downloadable!]
  11. Norman Swanson & Valentina Corradi, 2006. "Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes," Departmental Working Papers 200618, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  12. Minford, Patrick & Theodoridis, Konstantinos & Meenagh, David, 2007. "Testing a model of the UK by the method of indirect inference," Cardiff Economics Working Papers E2007/2, Cardiff University, Cardiff Business School, Economics Section, revised Apr 2008. [Downloadable!]
    Other versions:
  13. GONÇALVES, Silvia & WHITE, Halbert, 2001. "The Bootstrap of Mean for Dependent Heterogeneous Arrays," Cahiers de recherche 2001-19, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  14. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Conditional Distribution Tests In the Presence of Dynamic Misspecification," Departmental Working Papers 200311, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  15. Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, School of Economics and Management, University of Aarhus. [Downloadable!]
  16. Adrian Pagan & Hashem Pesaran, 2007. "Econometric Analysis of Structural Systems with Permanent and Transitory Shocks. Working paper #7," NCER Working Paper Series 7, National Centre for Econometric Research. [Downloadable!]
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