An algebraic construction of a class of one-dependent processes (Q1823539)

A discrete-time stochastic process \((X_ n)\) is called one-dependent if at any given time n, its past \((X_ k)_{k<n}\) is independent of its future \((X_ k)_{k>n}\). In contrast to the Markovian concept, no knowledge of the present value \(X_ n\) is assumed. An algebraic construction of stationary one-dependent two-valued stochastic processes is given which are not two-block factors of independent processes [see, e.g. \textit{S. Janson}, ibid. 12, 805-816 (1984; Zbl 0545.60080 )].