Statistical estimation of the Embedding Dimension of a dynamical system

International audienceWe consider a dynamical ergodic system defined as:Xt=ù(Xt-1,..., Xt-m0)where m0 is supposed to be unknown. X1,..., Xn being observed, we construct and study an estimate of m0 based on X1,..., XN, using the fact that m0 is a breaking point for the regularity of the distribution of (Xt-1,..., Xt-m0), m=1, 2,.... We present some simulations to illustrate our method and we discuss the computing problems