The author extends \textit{K. Urbanik's} results [Coll. Math. 12, 115-129 (1964; Zbl 0126.335)] to Banach space valued strictly stationary sequences. Such basic results for prediction as the Wold decomposition and the moving average representation of a completely nondeterministic component are deduced. There is a lack of examples here. A case of Gaussian stationary processes was established earlier by \textit{S. A. Chobanjan} and the reviewer [J. Multivariate Anal. 11, 69-80 (1981; Zbl 0454.60008)]. The paper is based on a very interesting application of the Ryll- Nardzewski conjecture proved independently by the author (Th.2.1) and \textit{J. Rosiński} [Bull. Acad. Polon. Sci., Sér. Sci. Math. 30, 379- 383 (1982; Zbl 0517.28011)]. The author's version is as follows: Let K be a Banach space and \(T_ 1\), \(T_ 2\) independent K-valued cylindrical random elements such that \(T_ 1+T_ 2\) is representable, i.e. there exists a K-valued random variable z for which \(y(z)=T_ 1y+T_ 2y\), where \(y\in K^*\). Then there exist \(b\in (K^*)'\) and K-valued random variables \(z_ 1,z_ 2\) such that for every \(y\in K^*\) \(y(z_ j)=T_ j(y)+(\)-1)\({}^ jb(y)\), where \(j=1,2\). This means that \(T_ 1\) and \(T_ 2\) are representable after translation.