Annual Report 2008.pdf - SAMSI

"The Asymptotic Structure of Nearly Unstable Nonnegative Integer-Valued AR(1) Models”
This paper considers nonnegative integer-valued autoregressive processes where the
autoregression parameter is close to unity. We consider the asymptotics of this `near unit root'
situation. The local asymptotic structure of the likelihood ratios of the model is obtained,
showing that the limit experiment is Poissonian. To illustrate the statistical consequences we
discuss efficient estimation of the autoregression parameter, and efficient testing for a unit root.
Keywords: branching process with immigration, integer-valued time series, Poisson limit
experiment, local-to-unity asymptotics, near unit root
Ishay Weissman
Technion - Israel Institute of Technology
ieriw01@ie.technion.ac.il
“On Dependence among Multivariate Extremes”
The dependence structure in multivariate extreme value distributions is completely determined
by the Pickands dependence function. If one wishes to represent the dependence by one
coefficient, then the literature offers several correlation-type coefficients, such as Kedall's tau,
Spearman's roh, etc. (for the bivariate case only). In this lecture we suggest the use of two
coefficients which are good for every dimension and possess some desired proprties.
Zhengjun Zhang
University of Wisconsin
zjz@stat.wisc.edu
“Extreme Value Copula and Applications”
This paper first establishes sufficient conditions under which multivariate max-stable processes
with infinite dimensional parameters can be approximated by multivariate maxima of moving
maxima processes with finite dimensional parameters. In the second part, a new family of
extreme value copula functions is introduced to provide a simple approximation to a max-stable
distribution. The estimators of the parameters in this new copula family are derived based on the
$k$th order statistics of ratios of Frechet random variables.
Chen Zhou
Erasmus University Rotterdam
zhou@few.eur.nl
“Portfolio Selection with Secondary Risk Indicators of Heavy Tailed Distributions”
Investing in diversified securities may result in a lower risk portfolio. The optimal construction
of the portfolio depends on the risk of individual securities as well as their dependence structure.
By modeling the individual security returns as heavy tailed and considering Value at Risk (VaR)
as the risk criterion, the scale parameter of the heavy tailed distribution turns to be the secondary
risk indicator alongside the primary risk indicator - the tail index. We study the portfolio