Multiple Outlier Detection in Samples with Exponential & Pareto Tails: Redeeming the Inward Approach & Detecting Dragon Kings

35 Pages Posted: 19 Aug 2015 Last revised: 23 Oct 2015

See all articles by Spencer Wheatley

Spencer Wheatley

ETH Zürich

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute

Date Written: August 17, 2015

Abstract

We consider the detection of multiple outliers in Exponential and Pareto samples -- as well as general samples that have approximately Exponential or Pareto tails, thanks to Extreme Value Theory. It is shown that a simple "robust'' modification of common test statistics makes inward sequential testing -- formerly relegated within the literature since the introduction of outward testing -- as powerful as, and potentially less error prone than, outward tests. Moreover, inward testing does not require the complicated type 1 error control of outward tests. A variety of test statistics, employed in both block and sequential tests, are compared for their power and errors, in cases including no outliers, dispersed outliers (the classical slippage alternative), and clustered outliers (a case seldom considered). We advocate a density mixture approach for detecting clustered outliers. Tests are found to be highly sensitive to the correct specification of the main distribution (Exponential/Pareto), exposing high potential for errors in inference. Further, in five case studies -- financial crashes, nuclear power generation accidents, stock market returns, epidemic fatalities, and cities within countries -- significant outliers are detected and related to the concept of 'Dragon King' events, defined as meaningful outliers of unique origin.

Keywords: Outlier Detection, Exponential sample, Pareto sample, Dragon King, Extreme Value Theory

JEL Classification: C12, C46, G01

Suggested Citation

Wheatley, Spencer and Sornette, Didier, Multiple Outlier Detection in Samples with Exponential & Pareto Tails: Redeeming the Inward Approach & Detecting Dragon Kings (August 17, 2015). Swiss Finance Institute Research Paper No. 15-28, Available at SSRN: https://ssrn.com/abstract=2645709 or http://dx.doi.org/10.2139/ssrn.2645709

Spencer Wheatley

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Didier Sornette (Contact Author)

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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