Nonparametric prediction of a Hilbert space valued random variable

Let $\text{ξ}{}_{\mathrm{t}}\text{, t ?}\text{R}$, be a Markovian, measurable, strictly stationary process taking values in a measurable space (E, $\text{B}$), and g a mapping from E into a separable Hilbert space H. A statistical nonparametric predictor of g(ξ_T+h) is studied in the paper. That predictor, based on the observations of the process between the times O and T generalizes the ‘predictogram’; its asymptotic consistency is proved and some applications are given.