Parametric and Bayesian non-parametric estimation of copulas
This thesis studies parametric and non-parametric methods of cop ula estimation with special focus on the Archimedean class of copu las. The first part proposes an estimation procedure which is indepen dent of the marginal distributions and performs well for one-parame ter or two-parameter families of copulas, where traditional methods give questionable results especially for small sample sizes. In the sec ond part we follow a Bayesian methodology and represent the copula density as a random piecewise constant, function. Under the presence of some data, we set up a probability distribution over the copula density and utilize Markov Chain Monte Carlo techniques to explore that distribution. The methodology is extended to perform shape preserving estimation of a univariate convex and monotone func tion that characterizes the copula. The estimated first and second derivatives of the function of interest must satisfy the restrictions that the theory imposes. All methods are illustrated with examples from simulated samples and a real-life dataset of the daily observations of the Dow-Jones and FTSE financial indices.