The Core, Periphery, and Beyond: Stock Market Comovements among EU and Non-EU Countries

We thank conference participants at the 2016 Financial Management Association and our discussant Fernando Moreira, and two anonymous referees for immensely helpful comments. We also thank Andrew Patton and James P. LeSage for sharing their MATLAB codes for computing quantile dependence. The authors of this paper are responsible for any errors or omissions. The Securities and Exchange Commission, as a matter of policy, disclaims responsibility for any private publication or statement by any of its employees. The views expressed herein are those of the authors and do not necessarily reflect the views of the Commission or the authors\u27 colleagues on the staff of the Commission

A new index to measure positive dependence in trivariate distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We introduce a new index to detect dependence in trivariate distributions. The index is based on the maximization of the coefficients of directional dependence over the set of directions. We show how to calculate the index using the three pairwise Spearman's rho coefficients and the three common 3-dimensional versions of Spearman's rho. We obtain the asymptotic distributions of the empirical processes related to the estimators of the coefficients of directional dependence and also we derive the asymptotic distribution of our index. We display examples where the index identifies dependence undetected by the aforementioned 3-dimensional versions of Spearman's rho. The value of the new index and the direction in which the maximal dependence occurs are easily computed and we illustrate with a simulation study and a real data set. (C) 2012 Elsevier Inc. All'rights reserved.We introduce a new index to detect dependence in trivariate distributions. The index is based on the maximization of the coefficients of directional dependence over the set of directions. We show how to calculate the index using the three pairwise Spearma115481495FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [10/51940-5]CNPq [485999/2007-2, 476501/2009-1]10/51940-5485999/2007-2; 476501/2009-

Asymptotic Conditional Distribution of Exceedance Counts: Fragility Index with Different Margins

Let $\bm X=(X_1,...,X_d)$ be a random vector, whose components are not necessarily independent nor are they required to have identical distribution functions $F_1,...,F_d$. Denote by $N_s$ the number of exceedances among $X_1,...,X_d$ above a high threshold $s$. The fragility index, defined by $FI=\lim_{s\nearrow}E(N_s\mid N_s>0)$ if this limit exists, measures the asymptotic stability of the stochastic system $\bm X$ as the threshold increases. The system is called stable if $FI=1$ and fragile otherwise. In this paper we show that the asymptotic conditional distribution of exceedance counts (ACDEC) $p_k=\lim_{s\nearrow}P(N_s=k\mid N_s>0)$, $1\le k\le d$, exists, if the copula of $\bm X$ is in the domain of attraction of a multivariate extreme value distribution, and if $\lim_{s\nearrow}(1-F_i(s))/(1-F_\kappa(s))=\gamma_i\in[0,\infty)$ exists for $1\le i\le d$ and some $\kappa\in{1,...,d}$. This enables the computation of the FI corresponding to $\bm X$ and of the extended FI as well as of the asymptotic distribution of the exceedance cluster length also in that case, where the components of $\bm X$ are not identically distributed

Evolution of the Dependence of Residual Lifetimes

We investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given

Worst VaR scenarios with given marginals and measures of association

This paper studies the problem of finding best-possible upper bounds on the Value-at-Risk for a function of two random variables when the marginal distributions are known and additional nonparametric information on the dependence structure, such as the value of a measure of association, is available. The same problem for the Tail-Value-at-Risk is also briefly discussed