Statistical estimation of the embedding dimension of a dynamical system

We consider a dynamical ergodic system defined as: X-t = psi(Xt-1,..., Xt-mo), where m(o) is supposed to be unknown. X-1,...,X-n being observed, we constr uct and study an estimate of m(o) based on X-1,...,X-Nl, using the fact tha t m(o) is a breaking point for the regularity of the distribution of (Xt-1, ...,Xt-m), m = 1, 2,.... We present some simulations to illustrate our meth od and we discuss the computing problems.