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Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models

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Author Info
Silvia Goncalves (University of Montreal)
Halbert White (University of California, San Diego)

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Abstract

The bootstrap is an increasingly popular method for performing statistical inference. This paper provides the theoretical foundation for using the bootstrap as a valid tool of inference for quasi-maximum likelihood estimators (QMLE). We provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes. We apply our results to two block bootstrap methods, the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) and the stationary bootstrap of Politis and Romano (1994), and prove the first order asymptotic validity of the bootstrap approximation to the true distribution of QML estimators. Further, these block bootstrap methods are shown to provide heteroskedastic and autocorrelation consistent standard errors for the QMLE, thus extending the already large literature on robust inference and covariance matrix estimation. We also consider bootstrap testing. In particular, we prove the first order asymptotic validity of the bootstrap distribution of a suitable bootstrap analog of a Wald test statistic for testing hypotheses.

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Publisher Info
Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2000-32.

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Date of creation: 01 Dec 2000
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Handle: RePEc:cdl:ucsdec:2000-32

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Related research
Keywords: block bootstrap; quasi maximum likelihood estimator; nonlinear dynamic model; near epoch dependence; Wald test;

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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. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc. [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. 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:
  4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  5. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October. [Downloadable!] (restricted)
  6. 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!]
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  7. 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.
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  8. 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)
  9. Sílvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO. [Downloadable!]
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  10. repec:cup:etheor:v:12:y:1996:i:1:p:187-97 is not listed on IDEAS
  11. repec:cup:etheor:v:7:y:1991:i:2:p:213-21 is not listed on IDEAS
  12. 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!]
  13. 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:
  14. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July. [Downloadable!] (restricted)
  15. 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)
  16. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June. [Downloadable!]
  17. 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)
  18. Shao, Jun, 1992. "Bootstrap variance estimators with truncation," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 95-101, September. [Downloadable!] (restricted)
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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. 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!]
  2. 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!]
    Other versions:
  3. Stan Hurn, 2004. "Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity," Econometric Society 2004 Australasian Meetings 348, Econometric Society. [Downloadable!]
    Other versions:
  4. 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)
  5. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics. [Downloadable!]
  6. 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:
  7. 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:
  8. 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!]
  9. 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!]
  10. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  11. 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!]
    Other versions:
  12. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Specification Tests for Diffusion Processes," Departmental Working Papers 200321, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  13. 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!]
  14. 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:
  15. 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:
  16. 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!]
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