9:30 Vine copulas
Vine copulas (also called the pair-copula construction) have been applied recently for finance asset return and other data, see e.g. Kurowicka and Joe (2011). d-dimensional vine copulas can cover flexible dependence structures through the specification of d-1 bivariate marginal copulas at level 1 and (d-1)(d-2)/2 bivariate conditional copulas at higher levels; at level l for l=2,… d-1, there are d-l bivariate conditional copulas that condition on l-1 variables. Vine copulas include multivariate normal and t copulas as special cases, but can also cover reflection asymmetry and have upper/lower tail dependence parameters being different for each bivariate margin (i, j). Joe et al. (2010) show that in order for a vine copula to have tail dependence for all bivariate margins, it is only necessary for the bivariate copulas in level 1 to have tail dependence and it is not necessary for the conditional bivariate copulas in levels 2,… d-1 to have tail dependence. Hence, for high-dimensional data, the number of dependence parameters can be reduced by considering truncated vines where conditional copulas are all independence copulas after level l.
11:00 Cofee/Tea and Refreshments
11:30 CDVine package by Schepsmeier and Brechmann
In this session we will describe and illustrate the features of the R package CDVine by Schepsmeier and Brechmann (2011).
14:00 Fitting vine copulas to financial return data
In this lecture we will use the software CDVine for the analysis of multivariate financial return data. We will consider a few European market indexes: CAC40 France, DAX Germany, OSEAX Norway, SMI Switzerland and FTSE England. Before proceeding to the vine copulas fitting via the CDVine package, we will implement diagnostics for dependence and reflection asymmetry to motivate the use of vine copulas with asymmetrical dependence for multivariate financial return data.
- Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44:182–198.
- Joe, H., Li, H., and Nikoloulopoulos, A. K. (2010). Tail dependence functions and vine copulas. Journal of Multivariate Analysis, 101:252–270.
- Kurowicka, D. and Joe, H. (2011). Dependence Modeling - Handbook on Vine Copulae. World Scientific Publishing Co, Singapore.
- Nikoloulopoulos, A. K., Joe, H., and Li, H. (2012). Vine copulas with asymmetric tail dependence and applications to financial return data. Computational Statistics and Data Analysis, 56:3659–3673.
- Schepsmeier, U. and Brechmann, E. C. (2011). CDVine: Statistical inference of C- and D-vine copulas. R package version 1.2.