Micro Correlations and Tail Dependence

Roger Cooke, Carolyn Kousky and Harry Joe
Additional contact information
Carolyn Kousky: Resources for the Future, Washington, USA
Harry Joe: Department of Statistics, University of British Columbia, Canada

Chapter 5 in Dependence Modeling:Vine Copula Handbook, 2010, pp 89-112 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractAn elementary though seemingly underappreciated finding shows that small global correlations are amplified by aggregation. We observe this behavior in flood damage claims in the US. We also observe that upper tail dependence seems to be amplified by aggregation in these data. We seek to understand this behavior. For sums of exponential variables which are conditionally independent given a gamma-distributed rate, we derive explicit expressions for upper tail dependence and prove that it goes to one as the number of summands goes to infinity, and that the lower tail dependence is zero. We also study sums of events under a latent variable model, where each event occurs if a uniform variable exceeds a threshold, and all uniform variables are conditionally independent given a “latent variable”. We obtain a necessary and sufficient condition for strong asymptotic upper tail dependence as the number of summands goes to infinity. Curiously, the normal copula satisfies this condition, although it is not tail dependent via the usual definition. Thus, sums of events under the normal copula latent variable model have upper tail dependence increasing to 1. We also identify tail dependent-like behavior in finite sums of events with the latent variable model.

Keywords: Dependence Modeling; Joint Distributions; Copulae; Vines; Graphical Models; PCC (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789814299886_0005 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789814299886_0005 (text/html)
Ebook Access is available upon purchase.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:wschap:9789814299886_0005

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().