This paper aims to present copulas, as a modeling tool which will give the 'richer' dependency structures than the use of linear correlation. The paper presents definitions and basic properties of the copula function. Discusses its relationship with the basic types of dependencies used in risk management i.e. comonotonicity, countermonotonicity, independence and linear dependence and the basic measures of dependence (Pearson's correlation, Kendall's rank correlation, Spearman's rank correlation, Blomqvist's beta, upper (lower) tail dependence parameter). Then selected family of copulas have been characterized and is an example of construction of two-dimensional dis- tribution, where the marginal distributions are known and the Kendall's rank correlation between them. Calculations and graphs were performed using the package „R”.
The aim of the paper is to analyse the conditional dependence structure between precious metal returns using a copula-DCC-GARCH approach. Conditional correlation matrices are used to identify the states of the precious metals market by assuming that a given state of the market corresponds to a typical pattern of the conditional dependence structure. Cluster analysis allows for pointing at transition points between the market states, that is the points of drastic change in the conditional dependence structure. The application of the methodology described above to the period between 1997 and 2013 indicates three market states of four major precious metals (gold, silver, platinum and palladium). The results obtained reveal a sudden increase in dependencies between precious metals at the turn of April and May 2004.
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W pracy analizowano warunkową strukturę zależności na rynku metali szlachetnych z wykorzystaniem modeli copula-DCC-GARCH. Na podstawie warunkowych macierzy korelacji rozpoznano stany rynku metali szlachetnych. W tym celu przyjęto, że określonemu stanowi rynku odpowiada typowy wzór warunkowej struktury zależności. Momenty przejścia pomiędzy poszczególnymi stanami odpowiadające nagłym (drastycznym) zmianom w warunkowej strukturze zależności zidentyfikowano, wykorzystując metody grupowania. Zastosowanie opisanej metodologii pozwoliło w okresie od 1997 r. do 2013 r. wyodrębnić trzy stany rynku czterech metali szlachetnych (złoto, srebro, platyna, pallad). Badania wskazały także na znaczny wzrost zależności między rozważanymi metalami na przełomie kwietnia i maja 2004 r.
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