Time-varying joint distribution through copulas

Time-varying joint distribution through copulas

This paper deals with the analysis of temporal dependence in multivariate time series. The dependence structure between the marginal series is modelled through the use of copulas which, unlike the correlation matrix, give a complete description of the joint distribution. The parameters of the copula function vary through time following certain evolution equations depending on their previous val...

Random variables, joint distribution functions, and copulas

If G is an n-dimensional joint distribution function with 1-dimensional margins F1,...,Fn, then there exists a function C (called an "w-copula") from the unit »-cube to the unit interval such that G(xx, ..., xn) = C(F1(x1), ..., Fn(xn)) for all real n-tuples (xlt ..., xn). The paper is devoted to an investigation of the structure and properties of n-copulas and their connection with random vari...

A threshold model for time varying copulas

We develop threshold models that allow copula functions or their association parameters changing across time. The number and location of thresholds is assumed unknown. We use a Markov chain Monte Carlo strategy combined with Laplace estimates that evaluate the required marginal densities for a given model. We apply our methodology to financial time series emphasizing the ability to improve esti...

Extreme distribution functions of copulas

Time-dependent copulas

For the study of dynamic dependence structures, we introduce the concept of pseudo-copulas, extending Patton’s (2001a) definition of conditional copulas, and state the equivalent of Sklar’s theorem for pseudo-copulas. We establish asymptotic normality of nonparametric estimators of the pseudo-copulas under strong mixing assumptions, and discuss applications to specification tests. We complement...