Tail index estimation in the presence of long-memory dynamics
Most tail index estimators are formulated under assumptions of weak serial dependence, but nevertheless are applied in practice to long-range dependent time series data. This issue arises because for many time series found in teletraffic and financial econometric applications, both heavy tails and long memory are prevalent features. For a certain class of Heavy-Tail Long-Memory (HTLM) processes, McElroy and Politis (2007a) and Jach et al. (2011) found that the probabilistic behavior of the sample mean depends delicately on the interplay of the tail index and the long memory parameter. In contrast, results in Kulik and Soulier (2011) indicate that the sample quantiles for a related HTLM process are unaffected by long-range dependence. Motivated by these results, we undertake an extensive numerical study to compare the finite-sample performance of several tail index estimators–both those based on sample quantiles, such as the Hill and DEdH (Hill (1975) and Dekkers et al. (1989)) as well as those based on moments, e.g. Meerschaert and Scheffler (1998)–in the HTLM context. Our results largely confirm and expand those of Kulik and Soulier (2011), in that the Hill and DEdH estimators perform well despite the presence of long memory.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 56 (2012)
Issue (Month): 2 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/csda|
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.:
- Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
- Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
- Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
- T. Rachev, Svetlozar & Samorodnitsky, Gennady, 2001. "Long strange segments in a long-range-dependent moving average," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 119-148, May.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:266-282. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.