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The Bootstrap Of The Mean For Dependent Heterogeneous Arrays

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Author Info
Gon alves, S lvia
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 K nsch (1989, Annals of Statistics 17, 1217 1241) and Liu and Singh (1992, in R. LePage L. Billiard (eds.), Exploring the Limits of the Bootstrap, 224 248) and the stationary bootstrap of Politis and Romano (1994a, Journal of the American Statistical Association 89, 1303 1313). 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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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 06 (December)
Pages: 1367-1384
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:18:y:2002:i:06:p:1367-1384_18

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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. 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. 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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  3. 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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  4. 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)
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  5. 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!]
  6. 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)
  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. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January. [Downloadable!] (restricted)
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  10. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June. [Downloadable!]
  11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [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. Joseph P. Romano & Michael Wolf, 2002. "Improved Nonparametric Confidence Intervals in Time Series Regressions," Economics Working Papers 635, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  2. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics. [Downloadable!]
  3. 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!]
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  4. 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:
  5. 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!]
  6. 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:
  7. 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!]
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