Discrete systems with memory (e.g. AR-N systems)

Describe the feature you'd like to have

See discussion here. It would be nice to have a dedicated implementation of DiscreteDynamicalSystemWithMemory, which could iterate systems where the next state depends on n previous time steps. This would allow defining for example autoregressive systems.

In CausalityTools.jl, I circumvent the lack of this type by defining each system as a struct that allocates memory containers that are updated as the system is iterated. For systems with stochastic components, these containers also store a reference to a random number generator, so that trajectories are reproducible.

If possible, sketch out an implementation strategy

Implement the approach described above, somehow. I'll revisit this when I'm done with the CausalityTools v2.0 release and after application deadlines.

Start with the existing dynamical-system types and iteration API, then read the linked CausalityTools.jl discussion and the proposed DiscreteDynamicalSystemWithMemory concept. Done means supporting systems whose next state depends on n previous steps, including autoregressive examples and reproducible stochastic trajectories.