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The Bootstrap Of The Mean For Dependent Heterogeneous Arrays

  • Gon alves, S lvia
  • White, Halbert

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. A0501n purpose of this paper is thus to 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. The results apply to the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) as well as to the stationary bootstrap of Politis and Romano (1994). 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. Actuellement, les conditions assurant la validité des méthodes de bootstrap pour la moyenne d'échantillon des (possiblement hétérogènes) fonctions de dépendance d'époque proche (DEP) des processus de mixage sont inconnues. Ainsi, un des objectifs principaux de cet article est d'établir la validité du bootstrap dans ce contexte, en élargissant l'applicabilité des méthodes de bootstrap à une classe de processus largement adéquats pour les applications en économie et en finance. Les résultats se rapportent au bootstrap de blocs mouvants de Künsch (1989) et Liu et Singh (1992), de même qu'au bootstrap stationnaire de Politis et Romano (1994). Plus particulièrement, nous démontrons que la consistance de l'estimateur de variance du bootstrap pour la moyenne d'échantillon résiste à l'hétéroscédasticité et à la dépendance de forme inconnue. La validité asymptotique de premier ordre de l'approximation du bootstrap à la distribution actuelle de la moyenne d'échantillon est également démontrée dans ce contexte DEP hétérogène.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 06 (December)
Pages: 1367-1384

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Handle: RePEc:cup:etheor:v:18:y:2002:i:06:p:1367-1384_18
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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. 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.
  3. 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.
  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.
  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.
  6. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  7. Hansen, Bruce E., 1991. "GARCH(1, 1) processes are near epoch dependent," Economics Letters, Elsevier, vol. 36(2), pages 181-186, June.
  8. 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.
  9. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  10. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  11. repec:cup:etheor:v:7:y:1991:i:2:p:213-21 is not listed on IDEAS
  12. 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.
  13. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June.
  14. 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.
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