On Functional Central Limit Theorems for Dependent, Heterogeneous Tail Arrays with Applications to Tail Index and Tail Dependence Estimators
AbstractWe 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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Bibliographic InfoPaper provided by Florida International University, Department of Economics in its series Working Papers with number 0607.
Length: 31 pages
Date of creation: Jul 2006
Date of revision:
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 and Methodology: General - - - Other
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-07-21 (All new papers)
- NEP-ECM-2006-07-21 (Econometrics)
- NEP-ETS-2006-07-21 (Econometric Time Series)
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