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On robust tail index estimation for linear Long-memory processes

Type of Publication: Journal article
Author: Beran, Jan; Das, Bikramjit; Schell, Dieter
Year of publication: 2012
Published in: Journal of Time Series Analysis ; 33 (2012), 3. - pp. 406-423. - ISSN 0143-9782. - eISSN 1467-9892
DOI (citable link): https://dx.doi.org/10.1111/j.1467-9892.2011.00774.x
Summary:
We consider robust estimation of the tail index α for linear long-memory processes inline image with i.i.d. innovations εj following a symmetric α-stable law (1 < α < 2) and coefficients aj ∼ c·j−βinline image. Estimates based on the left and right tail respectively are obtained together with a combined statistic with improved efficiency, and a test statistic comparing both tails. Asymptotic results are derived. Simulations illustrate the finite sample performance.
Subject (DDC): 510 Mathematics
Keywords: Long memory, infinite variance, tail index, M-estimation
Bibliography of Konstanz: Yes

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BERAN, Jan, Bikramjit DAS, Dieter SCHELL, 2012. On robust tail index estimation for linear Long-memory processes. In: Journal of Time Series Analysis. 33(3), pp. 406-423. ISSN 0143-9782. eISSN 1467-9892. Available under: doi: 10.1111/j.1467-9892.2011.00774.x

@article{Beran2012robus-23238, title={On robust tail index estimation for linear Long-memory processes}, year={2012}, doi={10.1111/j.1467-9892.2011.00774.x}, number={3}, volume={33}, issn={0143-9782}, journal={Journal of Time Series Analysis}, pages={406--423}, author={Beran, Jan and Das, Bikramjit and Schell, Dieter} }

We consider robust estimation of the tail index α for linear long-memory processes inline image with i.i.d. innovations εj following a symmetric α-stable law (1 < α < 2) and coefficients aj ∼ c·j−βinline image. Estimates based on the left and right tail respectively are obtained together with a combined statistic with improved efficiency, and a test statistic comparing both tails. Asymptotic results are derived. Simulations illustrate the finite sample performance. Journal of Time Series Analysis ; 33 (2012), 3. - S. 406-423 Beran, Jan Beran, Jan Schell, Dieter On robust tail index estimation for linear Long-memory processes 2012 terms-of-use Das, Bikramjit 2013-05-15T07:26:32Z Das, Bikramjit eng Schell, Dieter 2013-05-15T07:26:32Z

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