  Reachability analysis is a powerful tool for computing the set of states or
outputs reachable for a system. While previous work has focused on systems
described by state-space models, we present the first methods to compute
reachable sets of ARMAX models - one of the most common input-output models
originating from data-driven system identification. The first approach we
propose can only be used with dependency-preserving set representations such as
symbolic zonotopes, while the second one is valid for arbitrary set
representations but relies on a reformulation of the ARMAX model. By analyzing
the computational complexities, we show that both approaches scale
quadratically with respect to the time horizon of the reachability problem when
using symbolic zonotopes. To reduce the computational complexity, we propose a
third approach that scales linearly with respect to the time horizon when using
set representations that are closed under Minkowski addition and linear
transformation and that satisfy that the computational complexity of the
Minkowski sum is independent of the representation size of the operands. Our
numerical experiments demonstrate that the reachable sets of ARMAX models are
tighter than the reachable sets of equivalent state space models in case of
unknown initial states. Therefore, this methodology has the potential to
significantly reduce the conservatism of various verification techniques.
