  We consider statistical learning question for $\psi$-weakly dependent
processes, that unifies a large class of weak dependence conditions such as
mixing, association,$\cdots$ The consistency of the empirical risk minimization
algorithm is established. We derive the generalization bounds and provide the
learning rate, which, on some H{\"o}lder class of hypothesis, is close to the
usual $O(n^{-1/2})$ obtained in the {\it i.i.d.} case. Application to time
series prediction is carried out with an example of causal models with
exogenous covariates.
