Modelling Multivariate Dependence and Extremes
Funded by Free University of Bozen-Bolzano.
Participants (at UNIBZ): F. Durante (PI), F.M.L. Di Lascio, E. Foscolo, R. Pappadà (Jan-June 2014)
External participants: P. Jaworski (University of Warsaw, Poland), G. Salvadori (Università del Salento, Italy)
Period: Oct 2013 - Sept 2016.
Abstract: In most situations, we are not only confronted with one single source of risk or one single risk, but with several sources of risk or combinations of risks. As such, assessing the overall risk requires to understand how to model and describe the dependence among the individual risks. In the past decades, classical statistical dependence models have been formulated in terms of regression models or Gaussian models, which have provided to be useful in a number of situations. Nevertheless, especially in the recent years, these models seem not to be adequate for capturing some characteristics of extreme phenomena (especially in a financial context). Recently, the concept of copula has become a standard tool in order to describe the dependence among random phenomena, since it allows to combine the marginal behaviour of different risk types into a joint description for all risk types by taking into account their interactions in a very flexible way. In this research project, we aim at developing specific theoretical and computational investigations about the use of copulas in order to deal with multivariate extreme events. Our final aim is to contribute to the development of risk management strategy in complex systems (ranging from economic risk to environmental risk). Specifically, the research project deals with the theoretical and computational investigations of the following topics: tail dependence (Goal 1), approximation methods for dependence (Goal 2), dependence-based cluster analysis (Goal 3). The above cited investigations could be of great use in the following areas: study of correlation and interdependence of economic phenomena (App 1), Environmental Risk Management (App 2), Biostatistics (Appl 3).
Publications
Book
F. Durante and C. Sempi. Principles of Copula Theory. CRC/Chapman& Hall, Boca Raton, FL, 2015. ISBN: 978-1-439-88442-3.
Articles in journals with Impact factor
F. Durante, J. Fernández-Sánchez, and C. Sempi. Multivariate patchwork copulas: a unified approach with applications to partial comonotonicity. Insurance Math. Econom., 53(3):897–905, 2013. DOI:10.1016/j.insmatheco.2013.10.010.
F. Durante, J. Fernández-Sánchez, and W. Trutschnig. Multivariate copulas with hairpin support. J. Multivariate Anal., 130:323–334, 2014. DOI: 10.1016/j.jmva.2014.06.009
F. Durante, E. Foscolo, P. Jaworski, and H. Wang. A spatial contagion measure for financial time series. Expert Syst. Appl., 41(8):4023–4034, 2014. DOI: 10.1016/j.eswa.2013.12.020.
F. Durante, R. Pappadà, and N. Torelli. Clustering of financial time series in risky scenarios. Adv. Data Anal. Classif., 8(4):359–376, 2014. DOI: 10.1007/s11634-013-0160-4.
F. Durante and O. Okhrin. Estimation procedures for exchangeable Marshall copulas with hydrological application. Stoch. Environ. Res Risk Assess., 29:205–226, 2015. DOI: 10.1007/s00477-014-0866-7.
F. Durante, J. Fernández-Sánchez, and R. Pappadà. Copulas, diagonals and tail dependence. Fuzzy Sets and Systems, in press. DOI: 10.1016/j.fss.2014.03.014.
F. Durante, R. Pappadà, and N. Torelli. Clustering of time series via non–parametric tail dependence estimation. Statist. Papers, in press. DOI: 10.1007/s00362-014-0605-7.
F. Durante, J. Fernández-Sánchez, and W. Trutschnig. On the singular components of a copula. J. Appl. Probab., 52:1175-1182, 2015.
F. Durante, J. Fernández-Sánchez, J. Quesada-Molina, and M. Úbeda-Flores. Convergence results for patchwork copulas. European J. Oper. Res., 247(2):525–531, 2015. DOI: 10.1016/j.ejor.2015.06.028.
F. M. L. Di Lascio, F. Durante, and P. Jaworski. Truncation invariant copulas and a testing procedure. J. Stat. Comput. Simul., in press, 2015. DOI: 10.1080/00949655.2015.1110820.