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We consider the filter Yt = ∞ ∑ j=0 ajXt−j + 2t, t = 0,±1,±2, . . . and we study the asymptotic behaviour of the density of (Yt, Xt, . . . , Xt−k) when k tends to infinity. This problem is connected with the estimation of the aj ’s by an empirical maximum likelihood method. ∗LSTA, Université Paris VI Received by the editors April 1993 Revised July 1993 Communicated by M. Hallin AMS Mathematics Subject Classification : Primary 62M20, Secondary 62G05

Étude asymptotique de la densité associée `a un filtre d'ordre infini