  We consider stationary stochastic processes $X_n$, $n\in \mathbb{Z}$ such
that $X_0$ lies in the closed linear span of $X_n$, $n\neq 0$; following Ghosh
and Peres, we call such processes linearly rigid. Using a criterion of
Kolmogorov, we show that it suffices, for a stationary stochastic process to be
rigid, that the spectral density vanish at zero and belong to the Zygmund class
$\Lambda_{*}(1)$. We next give sufficient condition for stationary
determinantal point processes on $\mathbb{Z}$ and on $\mathbb{R}$ to be rigid.
Finally, we show that the determinantal point process on $\mathbb{R}^2$ induced
by a tensor square of Dyson sine-kernels is $\textit{not}$ linearly rigid.
