Next Article in Journal / Special Issue
On Bootstrap Inference for Quantile Regression Panel Data: A Monte Carlo Study
Previous Article in Journal
Right on Target, or Is it? The Role of Distributional Shape in Variance Targeting
Article Menu

Export Article

Open AccessArticle
Econometrics 2015, 3(3), 633-653; doi:10.3390/econometrics3030633

A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index

Department of Economics, University of Southampton, Bld 58 (Murray Bld), Highfield Campus, Southampton SO17 1BJ, UK
Academic Editor: Gabriel Montes-Rojas
Received: 14 July 2015 / Revised: 3 August 2015 / Accepted: 7 August 2015 / Published: 28 August 2015
(This article belongs to the Special Issue Quantile Methods)
View Full-Text   |   Download PDF [394 KB, uploaded 1 September 2015]   |  

Abstract

The extremal index (θ) is the key parameter for extending extreme value theory results from i.i.d. to stationary sequences. One important property of this parameter is that its inverse determines the degree of clustering in the extremes. This article introduces a novel interpretation of the extremal index as a limiting probability characterized by two Poisson processes and a simple family of estimators derived from this new characterization. Unlike most estimators for θ in the literature, this estimator is consistent, asymptotically normal and very stable across partitions of the sample. Further, we show in an extensive simulation study that this estimator outperforms in finite samples the logs, blocks and runs estimation methods. Finally, we apply this new estimator to test for clustering of extremes in monthly time series of unemployment growth and inflation rates and conclude that runs of large unemployment rates are more prolonged than periods of high inflation. View Full-Text
Keywords: asymptotic theory; clustering of extremes; extremal index; extreme value theory; order statistics asymptotic theory; clustering of extremes; extremal index; extreme value theory; order statistics
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Olmo, J. A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index. Econometrics 2015, 3, 633-653.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Econometrics EISSN 2225-1146 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top