Wiener and Masani describe a procedure for relating nonlinear prediction of a univariate random process to linear prediction of an infinite-variate process which may not be a Hilbert-space-valued process but may be Banach-space-valued instead. An algorithm for computation of the linear predictor and the generating function of a Banach-space-valued stationary stochastic process is obtained under an extension of the boundedness condition of Wiener and Masani on the spectral density of the process.
"An Algorithm for Linear Prediction of a Banach Space Valued Stationary Stochastic Process." Ann. Probab. 6 (5) 891 - 898, October, 1978. https://doi.org/10.1214/aop/1176995436