A Limit Theorem for Copulas
نویسندگان
چکیده
We characterize convergence of a sequence of d-dimensional random vectors by convergence of the one-dimensional margins and of the copula. The result is applied to the approximation of portfolios modelled by t-copulas with large degrees of freedom, and to the convergence of certain dependence measures of bivariate distributions. AMS 2000 Subject Classifications: primary: 60F05, 62H05 secondary: 60G50, 60G70
منابع مشابه
An Empirical Central Limit Theorem with applications to copulas under weak dependence
We state a multidimensional Functional Central Limit Theorem for weakly dependent random vectors. We apply this result to copulas. We get the weak convergence of the empirical copula process and of its smoothed version. The finite dimensional convergence of smoothed copula densities is also proved. A new definition and the theoretical analysis of conditional copulas and their empirical counterp...
متن کاملCharacterization of dependence of multidimensional Lévy processes using Lévy copulas
This paper suggests to use Lévy copulas to characterize the dependence among components of multidimensional Lévy processes. This concept parallels the notion of a copula on the level of Lévy measures. As for random vectors, a kind of Sklar’s theorem states that the law of a general multivariate Lévy process is obtained by combining arbitrary univariate Lévy processes with an arbitrary Lévy copu...
متن کاملTesting for equality between two copulas
We develop a test of equality between two dependence structures estimated through empirical copulas. We provide inference for independent or paired samples. The multiplier central limit theorem is used for calculating p-values of the Cramér-von Mises test statistic. Finite sample properties are assessed with Monte Carlo experiments. We apply the testing procedure on empirical examples in financ...
متن کاملLévy copulas: dynamics and transforms of Upsilon-type
Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced positive Lévy copulas. Together with the marginal Lévy measures they completely describe multivariate Lévy measures on R+ . In this paper, we show that any such Lévy copula defines it...
متن کاملThe Local Limit Theorem: A Historical Perspective
The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003