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The Bootstrap of Mean for Dependent Heterogeneous Arrays

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Author Info
GONÇALVES, Silvia
WHITE, Halbert

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Abstract

Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. Here we establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. Our results apply to two block bootstrap methods: the moving blocks bootstrap of Künsch ( 989) and Liu and Singh ( 992), and the stationary bootstrap of Politis and Romano ( 994). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context.

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File URL: http://hdl.handle.net/1866/359
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Publisher Info
Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2001-19.

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Length: 21 pages
Date of creation: 2001
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Handle: RePEc:mtl:montde:2001-19

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Related research
Keywords: block bootstra near ech dendence; same mean;

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Find related papers by JEL classification:
C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods
C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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. Hansen, Bruce E., 1991. "GARCH(1, 1) processes are near epoch dependent," Economics Letters, Elsevier, vol. 36(2), pages 181-186, June. [Downloadable!] (restricted)
  2. Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225. [Downloadable!] (restricted)
    Other versions:
  3. 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:
  4. Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Silvia Goncalves & Halbert White, 2000. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series 2000-32, Department of Economics, UC San Diego. [Downloadable!]
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  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  8. repec:cup:etheor:v:7:y:1991:i:2:p:213-21 is not listed on IDEAS
  9. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June. [Downloadable!]
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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. Silvia Goncalves & Halbert White, 2002. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series 2000-32R, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  2. Stan Hurn & Ralf Becker, 2006. "Testing for nonlinearity in mean in the presence of heteroskedasticity," Stan Hurn Discussion Papers 2006-02, School of Economics and Finance, Queensland University of Technology. [Downloadable!]
    Other versions:
  3. 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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