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Communications in Statistics. Stochastic Models Volume 13, 1997 - Issue 4
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Asymptotic behavior of hill's estimator for autoregressive data

Sidney Resnick Cornell University, School of ORIE, Rhodes Hall, Ithaca, NY, 14853
&
Cătălin Stărică Department of Statistics, University of Pennsylvania The Wharton School, Steinberg Hall-Dietrich Hall, Philadelphia, PA, 19104
Pages 703-721 | Received 16 Aug 1996, Accepted 26 Mar 1997, Published online: 21 Mar 2007

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Mihyun Kim & Piotr Kokoszka. (2023) Asymptotic and finite sample properties of Hill-type estimators in the presence of errors in observations. Journal of Nonparametric Statistics 35:1, pages 1-18.
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Rongmao Zhang, Chenxue Li & Liang Peng. (2019) Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors. Econometric Reviews 38:2, pages 151-169.
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Karima Boualam & Youcef Berkoun. (2017) Hill's estimator under weak dependence. Communications in Statistics - Theory and Methods 46:18, pages 9218-9229.
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A. Dematteo & S. Clémençon. (2016) On tail index estimation based on multivariate data. Journal of Nonparametric Statistics 28:1, pages 152-176.
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Laurens de Haan, Cécile Mercadier & Chen Zhou. (2016) Adapting extreme value statistics to financial time series: dealing with bias and serial dependence. Finance and Stochastics 20:2, pages 321-354.
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Jonathan B. Hill. (2012) Least tail‐trimmed squares for infinite variance autoregressions. Journal of Time Series Analysis 34:2, pages 168-186.
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P. Y. Lai & Stephen M. S. Lee. (2012) Estimation of central shapes of error distributions in linear regression problems. Annals of the Institute of Statistical Mathematics 65:1, pages 105-124.
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Chenhua Zhang & William P. McCormick. (2011) Asymptotic properties of the tail distribution and Hill’s estimator for shot noise sequence. Extremes 15:4, pages 407-435.
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Moosup Kim & Sangyeol Lee. (2012) Change point test of tail index for autoregressive processes. Journal of the Korean Statistical Society 41:3, pages 305-312.
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Chenhua Zhang. (2011) Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations. Statistics & Probability Letters 81:12, pages 1961-1969.
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Moosup Kim & Sangyeol Lee. (2009) Test for tail index change in stationary time series with Pareto-type marginal distribution. Bernoulli 15:2.
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Greg N. GregoriouAndreas A. Jobst. 2009. Operational Risk toward Basel III. Operational Risk toward Basel III 23 68 .
Holger Rootzén. (2009) Weak convergence of the tail empirical process for dependent sequences. Stochastic Processes and their Applications 119:2, pages 468-490.
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Moosup Kim & Sangyeol Lee. (2008) Estimation of a tail index based on minimum density power divergence. Journal of Multivariate Analysis 99:10, pages 2453-2471.
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Holger Drees. (2008) Some aspects of extreme value statistics under serial dependence. Extremes 11:1, pages 35-53.
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Andreas Jobst. (2007) Operational Risk: The Sting is Still in the Tail But the Poison Dependson the Dose. IMF Working Papers 07:239, pages 1.
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. 2007. Statistical Analysis of Extreme Values. Statistical Analysis of Extreme Values 207 226 .
Sidney Resnick. (2016) On the foundations of multivariate heavy-tail analysis. Journal of Applied Probability 41:A, pages 191-212.
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István Berkes, Lajos Horváth & Piotr Kokoszka. (2003) ESTIMATION OF THE MAXIMAL MOMENT EXPONENT OF A GARCH(1,1) SEQUENCE. Econometric Theory 19:04.
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Peter Hall, Liang Peng & Qiwei Yao. (2002) Moving-maximum models for extrema of time series. Journal of Statistical Planning and Inference 103:1-2, pages 51-63.
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Holger Drees. 2002. Empirical Process Techniques for Dependent Data. Empirical Process Techniques for Dependent Data 325 342 .
Holger Drees. 2001. Encyclopedia of Environmetrics. Encyclopedia of Environmetrics.
Jaap L. Geluk, Liang Peng & Casper G. de Vries. (2016) Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series. Advances in Applied Probability 32:4, pages 1011-1026.
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Holger Drees. (2000) Weighted approximations of tail processes for $\beta$-mixing random variables. The Annals of Applied Probability 10:4.
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Sándor Csörgő & László Viharos. 1998. Asymptotic Methods in Probability and Statistics. Asymptotic Methods in Probability and Statistics 833 881 .
Andreas A. Jobst. (2007) Constraints of Operational Risk Measurement and the Treatment of Operational Risk Under the New Basel Framework. SSRN Electronic Journal.
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Yves Dominicy, Pauliina Ilmonen & David Veredas. (2013) A Multivariate Hill Estimator. SSRN Electronic Journal.
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Jonathan B. Hill. (2012) Tail Index Estimation for a Filtered Dependent Time Series. SSRN Electronic Journal.
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