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Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Strochastic Processes with an Application

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  • Jonathan B. Hill

    ()
    (Department of Economics, Florida International University)

Abstract

We develop a non-parametric test of tail-specific extremal serial dependence for possibly heavy-tailed time series. The test statistic is asymptotically chi-squared under a null of "extremal white noise", as long as extremes of the time series are Near-Epoch-Dependent on the extremes of some mixing process. The theory covers ARFIMA, FIGARCH, bilinear, and Extremal Threshold processes, and a wide range of nonlinear distributed lags. In this setting the test statistic obtains an asymptotic power of one under the alternative. Of separate interest, we deliver a joint distribution limit for an arbitrary vector of tail index estimators under extraordinarily gene ral conditions, complete with a consistent kernel estimator of the covariance matrix. We apply tail specific tests to equity market and exchange rate returns data.

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File URL: http://casgroup.fiu.edu/pages/docs/2247/1275232517_05-13.pdf
File Function: Revised version, 2006
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Bibliographic Info

Paper provided by Florida International University, Department of Economics in its series Working Papers with number 0513.

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Length: 30 pages
Date of creation: Aug 2005
Date of revision:
Handle: RePEc:fiu:wpaper:0513

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Keywords: extremal dependence; white-noise; near-epoch-dependence; regular variation; infinite variance; portmanteau test;

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  19. Jonathan B. Hill, 2005. "On Tail Index Estimation Using Dependent,Heterogenous Data," Working Papers 0512, Florida International University, Department of Economics.
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