Roberta Pappadà

Copulas, diagonals, and tail dependence

We present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence. Moreover, we present the tail concentration function (which depends on the diagonal section of a copula) as a tool to give a description of tail dependence at finite scale. The tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space. Moreover, it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior.

Clustering of financial time series in risky scenarios

A methodology is presented for clustering financial time series according to the association in the tail of their distribution. The procedure is based on the calculation of suitable pairwise conditional Spearman’s correlation coefficients extracted from the series. The performance of the method has been tested via a simulation study. As an illustration, an analysis of the components of the Italian FTSE–MIB is presented. The results could be applied to construct financial portfolios that can manage to reduce the risk in case of simultaneous large losses in several markets.

Quantification of the environmental structural risk with spoiling ties: is randomization worthwhile?

Many recent works show that copulas turn out to be useful in a variety of different applications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) adjustments and truncations, and eventually may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to adopt suitable randomization procedures: here three different strategies are outlined. The goal of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it is investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering applications. Practical advices and warnings about the use of randomization techniques are hence given.

Spin-off Extreme Value and Archimedean copulas for estimating the bivariate structural risk

In environmental applications, the estimation of the structural risk is fundamental. Beside the knowledge of the physical response of the structure to the loads of interest, a statistical model for the behavior of the input variables is generally required, possibly accounting for the fact that these variables are usually non-independent. For this purpose, a multivariate approach based on copulas is adopted in this paper. In particular, the following classes of dependence structures are often used in practice: the Extreme Value copulas, and the Archimedean copulas. However, how to properly select a suitable Extreme Value or Archimedean copula is a problem open to many solutions. As a viable one, this work shows how two semi-parametric approximations to, respectively, Extreme Value and Archimedean copulas, can be used in order to circumvent the troublesome selection issue in the estimation of the structural risk. Suitable simulation studies are performed, in order to check and evaluate the performance of the approximating techniques introduced in this work.

Cluster analysis of time series via Kendall distribution

We present a method to cluster time series according to the calculation of the pairwise Kendall distribution function between them. A case study with environmental data illustrates the introduced methodology.

Copula–based clustering methods

We review some recent clustering methods based on copulas. Specifically, in the dissimilarity–based clustering framework, we describe and compare methods based on concordance or tail-dependence concept. An illustration is hence provided by using a time series dataset formed by the constituent data of the S&P 500 observed during the financial crisis of 2007-2008. Next, in the likelihood–based clustering framework, we present and discuss a clustering algorithm based on copula and called CoClust. Here, an application to the gene expression profiles of human tumour cell lines is provided to describe the methodology. Finally, a comparison between the two different approaches is performed through a case study on environmental data.

A portfolio diversification strategy via tail dependence clustering

We provide a two-stage portfolio selection procedure in order to increase the diversification benefits in a bear market. By exploiting tail dependence-based risky measures, a cluster analysis is carried out for discerning between assets with the same performance in risky scenarios. Then, the portfolio composition is determined by fixing a number of assets and by selecting only one item from each cluster. Empirical calculations on the EURO STOXX 50 prove that investing on selected assets in trouble periods may improve the performance of risk-averse investors.

A Graphical Tool for Copula Selection Based on Tail Dependence

In many practical applications, the selection of copulas with a specific tail behaviour may allow to estimate properly the region of the distribution that is needed at most, especially in risk management procedures. Here, a graphical tool is presented in order to assist the decision maker in the selection of an appropriate model for the problem at hand. Such a tool provides valuable indications for a preliminary overview of the tail features of different copulas which may help in the choice of a parametric model. Its use is illustrated under various dependency scenarios.

Maxima Units Search (MUS) Algorithm: Methodology and Applications

An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed. The procedure has already been satisfactorily applied for solving the label switching problem in Bayesian mixture models. Here we introduce it on its own and explore possible applications in different contexts.