  A set $P\subset \mathbb N$ is called predictive if for any zero entropy
finite-valued stationary process $(X_i)_{i\in \mathbb Z}$, $X_0$ is measurable
with respect to $(X_i)_{i\in P}$. We know that $\mathbb N$ is a predictive set.
In this paper we give sufficient conditions and necessary ones for a set to be
predictive. We also discuss linear predictivity, predictivity among Gaussian
processes and relate these to Riesz sets which arise in harmonic analysis.
