In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by asequence of stable distributions with indices alpha n - 2 than by a normal distribution. We discusswhen this happens and how much the convergence rate can be improved by using penultimate...

For an AR(1) process with ARCH(1) errors, we propose empirical likelihood tests for testing whether the sequence is strictly stationary but has infinte variance, or the sequence is an ARCH(1) sequence or the sequence is an iid sequence. Moreover, an empirical likelihood based confidence interval...

In general, risk of an extreme outcome in financial markets can be expressed as a function of the tail copula of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail copulas. Even for moderate dimension, nonparametrically estimating a tail...

Recently there has been an increasing interest in applying elliptical distributions to risk management. Under weak conditions, Hult and Lindskog (2002) showed that a random vector with an elliptical distribution is in the domain of attraction of a multivariate extreme value distribution. In this...

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptivemethod to choose the number of order statistics involved in an optimal way, balancing variance and biascomponents. Recently this has been achieved for the similar but somewhat less involved...

The paper characterizes first and second order tail behavior ofconvolutions of i.i.d. heavy tailed random variables with supporton the real line. The result is applied to the problem of riskdiversification in portfolio analysis and to the estimation of theparameter in a MA(1) model.

Internet auctions attract numerous agents, but only a few become active bidders. A major difficulty in the structural analysis of internet auctions is that the number of potential bidders is unknown. Under the independent private value paradigm (IPVP)the valuations of the active bidders form a...

The selection of upper order statistics in tail estimation is notoriously difficult. Methods that are based on asymptotic arguments, like minimizing the asymptotic MSE, do not perform well in finite samples. Here, we advance a data-driven method that minimizes the maximum distance between the...

We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the samplefraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methodsour procedure is fully self contained. In particular, the...

The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate...