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On Functional Central Limit Theorems for Dependent, Heterogeneous Tail Arrays with Applications to Tail Index and Tail Dependence Estimators

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Author Info
Jonathan Hill () (Department of Economics, Florida International University)

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Abstract

We establish functional central limit theorems for a broad class of dependent, heterogeneous tail arrays encountered in the extreme value literature, including extremal exceedances, tail empirical processes and tail empirical quantile processes. We trim dependence assumptions down to a minimum by constructing extremal versions of mixing and Near-Epoch-Dependence properties, covering mixing, ARFIMA, FIGARCH, bilinear, random coefficient autoregressive, nonlinear distributed lag and Extremal Threshold processes, and stochastic recurrence equations. Of practical importance our theory can be used to characterize the functional limit distributions of sample means and covariances of tail arrays, including popular tail index estimators, the tail quantile function, and multivariate extremal dependence measures under substantially general conditions.

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File URL: http://www.fiu.edu/orgs/economics/wp2006/06-07.pdf
File Format: application/pdf
File Function: Revised version, 2006
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Publisher Info
Paper provided by Florida International University, Department of Economics in its series Working Papers with number 0607.

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Length: 31 pages
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:fiu:wpaper:0607

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Related research
Keywords: Functional central limit theorem; extremal processes; tail empirical process; cadlag space; mixingale; near-epoch-dependence; regular variation; Hill estimator; tail dependence.;

Find related papers by JEL classification:
C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Other
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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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. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October. [Downloadable!]
    Other versions:
  2. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June. [Downloadable!]
  3. repec:cup:etheor:v:13:y:1997:i:3:p:353-67 is not listed on IDEAS
  4. Jonathan B. Hill, 2004. "Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Time Series with an Application," Econometrics 0411014, EconWPA, revised 09 Dec 2004. [Downloadable!]
  5. Stefan Mittnik & Svetlozar Rachev, 1993. "Modeling asset returns with alternative stable distributions," Econometric Reviews, Taylor and Francis Journals, vol. 12(3), pages 261-330. [Downloadable!] (restricted)
  6. Quintos, Carmela & Fan, Zhenhong & Phillips, Peter C B, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Blackwell Publishing, vol. 68(3), pages 633-63, July.
  7. 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)
  8. Einmahl, J.H.J. & Lin, T., 2003. "Asymptotic normality of extreme value estimators on C[0,1]," Discussion Paper 132, Tilburg University, Center for Economic Research. [Downloadable!]
  9. 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. [Downloadable!]
  10. 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:
  11. Rootzen, H. & Leadbetter, L. & De Haan, L., 1990. "Tail And Quantile Estimation For Strongly Mixing Stationary Sequences ," Papers 9024-a, Erasmus University of Rotterdam - Econometric Institute.
  12. Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, EconWPA, revised 27 May 2005. [Downloadable!]
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