  Hidden nonlocality is the phenomenon that entangled states can be local in
the standard Bell scenario but display nonlocality after local filtering.
However, there exist entangled states for which all measurement statistics can
be described via a local hidden variable model even after local filtering. In
this work we consider the scenario that measurement outcomes and settings of
Alice can influence measurements of Bob in subsequent time steps (and vice
versa), however, there is no signaling among them for measurements at the same
time step. We show that in this scenario states that only display local
statistics after local filtering remain local even when considering the
complete statistics of arbitrary sequences and therefore no advantage can be
gained by performing longer sequences in this scenario. We first determine the
extreme points of the polytope defined by the no-signaling conditions within
the same time step and the arrow-of-time constraints. Based on these results we
introduce a notion of locality and provide a complete representation of the
corresponding local polytope in terms of inequalities in the simplest scenario.
These results imply that in the scenario considered here there is no
nonlocality beyond hidden nonlocality. We further propose a device-dependent
Schmidt number witness and we compare our finding to known local models in the
sequential scenario.
