Practical Representations of Copula and Joint Density Estimates

Abstract

- A moment-based approximation methodology for estimating a copula density from bivariate observations is introduced. The resulting simple representation of the copula density is suitable for reporting purpose or carrying out further algebraic manipulation. Empirical copula density functions will also be determined from kernel density estimates. A technique for obtaining a joint density from marginal density estimates and a copula density is proposed as well. The Bernstein copula density approximants will be utilized for comparison purposes. The results are applied to two stocks’ closing prices and a stock’s price and its running maximum. In the latter case, the model is related to a Brownian motion process.