  Pickands dependence functions characterize bivariate extreme value copulas.
In this paper, we study the class of polynomial Pickands functions. We provide
a solution for the characterization of such polynomials of degree at most
$m+2$, $m\geq0$, and show that these can be parameterized by a vector in
$\mathbb{R}^{m+1}$ belonging to the intersection of two ellipsoids. We also
study the class of Bernstein approximations of order $m+2$ of Pickands
functions which are shown to be (polynomial) Pickands functions and
parameterized by a vector in $\mathbb{R}^{m+1}$ belonging to a polytope. We
give necessary and sufficient conditions for which a polynomial Pickands
function is in fact a Bernstein approximation of some Pickands function.
Approximation results of Pickands dependence functions by polynomials are
given. Finally, inferential methodology is discussed and comparisons based on
simulated data are provided.
