  Recent work has shown the effectiveness of tensor network methods for
computing large deviation functions in constrained stochastic models in the
infinite time limit. Here we show that these methods can also be used to study
the statistics of dynamical observables at arbitrary finite time. This is a
harder problem because, in contrast to the infinite time case where only the
extremal eigenstate of a tilted Markov generator is relevant, for finite time
the whole spectrum plays a role. We show that finite time dynamical partition
sums can be computed efficiently and accurately in one dimension using matrix
product states, and describe how to use such results to generate rare event
trajectories on demand. We apply our methods to the Fredrickson-Andersen (FA)
and East kinetically constrained models, and to the symmetric simple exclusion
process (SSEP), unveiling dynamical phase diagrams in terms of counting field
and trajectory time. We also discuss extensions of this method to higher
dimensions.
