arXiv subjects

Helena Ferreira

Publications and source records attributed to Helena Ferreira.

28 records · Page 2Linked to original sources

arXiv2012

Generating multivariate extreme value distributions

We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail dependence and extremal coefficients. Based on the obtained results for these coefficients, we propose a method to built multivariate extreme value distributions with prescribed tail/extremal coefficients. We illustrate the results with examples of simulation of these distributions.

math.PR↗

arXiv2012

Generalized madogram and pairwise dependence of maxima over two regions of a random field

Spatial environmental processes often exhibit dependence in their large values. In order to model such processes their dependence properties must be characterized and quantified. In this paper we introduce a measure that evaluates the dependence among extreme observations located in two separated regions of locations of R^2. We compute the range of this new dependence measure, which extends the existing λ-madogram concept, and compare it with extremal coefficients, finding generalizations of the known relations in pairwise approach. Estimators for this measure are introduced and asymptotic normality and strong consistency are shown. An application to the annual maxima precipitation in Portuguese regions is presented.

math.ST↗

arXiv2011

Fragility Index of block tailed vectors

Financial crises are a recurrent phenomenon with important effects on the real economy. The financial system is inherently fragile and it is therefore of great importance to be able to measure and characterize its systemic stability. Multivariate extreme value theory provide us such a framework through the \emph{fragility index} (Geluk \cite{gel+}, \emph{et al.}, 2007; Falk and Tichy, \cite{falk+tichy1,falk+tichy2} 2010, 2011). Here we generalize this concept and contribute to the modeling of the stability of a stochastic system divided into blocks. We will find several relations with well-known tail dependence measures in literature, which will provide us immediate estimators. We end with an application to financial data.

math.ST↗

arXiv2011

Extremal dependence: some contributions

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to assess the amount of dependence in $d$-variate random vectors based on bidimensional techniques. Very simple estimators will be stated and can be applied to the well-known \emph{stable tail dependence function}. Asymptotic normality and strong consistency will be derived too. An application to financial markets will be presented at the end.

math.ST↗

arXiv2011

Generalized Logistic Models and its orthant tail dependence

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn (1990), Joe and Hu (1996) and Fougères et al. (2009). The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li (2009).

math.PR↗

arXiv2010

On the multivariate upcrossings index

The notion of multivariate upcrossings index of a stationary sequence ${\bf{X}}=\{(X_{n,1},\ldots,X_{n,d})\}_{n\geq 1}$ is introduced and its main properties are derived, namely the relations with the multivariate extremal index and the clustering of upcrossings. Under asymptotic independence conditions on the marginal sequences of ${\bf{X}}$ the multivariate upcrossings index is obtained from the marginal upcrossings indices. For a class of stationary multidimensional sequences assumed to satisfy a mild oscillation restriction, the multivariate upcrossings index is computed from the joint distribution of a finite number of variables. The upcrossings index is calculated for two examples of bivariate sequences.

math.PR↗

arXiv2010

Dependence of multivariate extremes

We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with extremal index, to be independent or totally dependent. Those conditions involve first relations between the multivariate extremal indexes of the sequences and secondly a coefficient that measure the strength of dependence between both sub-vectors. The main results are illustrated with an auto-regressive sequence and a 3-dependent sequence.

math.PR↗

arXiv2010

Universality in DAX index returns fluctuations

In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, after normalization, the alpha positive fluctuations and alpha negative fluctuations. We use the Kolmogorov-Smirnov statistical test, as a method, to find the values of alpha that optimize the data collapse of the histogram of the alpha fluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are alpha+=0.50 and alpha-=0.48. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.

q-fin.ST↗

arXiv2010

Universal Fluctuations of the FTSE100

We compute the analytic expression of the probability distributions F{FTSE100,+} and F{FTSE100,-} of the normalized positive and negative FTSE100 (UK) index daily returns r(t). Furthermore, we define the alpha re-scaled FTSE100 daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, after normalization, the alpha positive fluctuations and alpha negative fluctuations. We use the Kolmogorov-Smirnov statistical test, as a method, to find the values of alpha that optimize the data collapse of the histogram of the alpha fluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are alpha+=0.55 and alpha-=0.55. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.

q-fin.ST↗

arXiv2010

Universal Fluctuations of AEX index

We compute the analytic expression of the probability distributions F{AEX,+} and F{AEX,-} of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the αre-scaled AEX daily index positive returns r(t)^αand negative returns (-r(t))^αthat we call, after normalization, the αpositive fluctuations and αnegative fluctuations. We use the Kolmogorov-Smirnov statistical test, as a method, to find the values of αthat optimize the data collapse of the histogram of the αfluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are α+=0.46 and α-=0.43. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.

q-fin.ST↗