You should probably try all four. There are some simple ways for you to do comparisons yourself. You can easily compare time-series models and the robustness of their training by using them to recursively predict the future by feeding their outputs back into themselves (regardless if they were trained in that fashion).

This will expose the properties of the eigenvalues of the model itself. Failure of a time-series model to match the larger eigenvalues of a system means it is failing the fundamentals and not able to capture the most basic global properties of the system you are trying to fit.

You don't necessarily have to do any fancy calculations. If the models fail to maintain the same qualitative patterns apparent in the original data over long time periods of self-input, then that means they are failing to capture the underlying dynamics. Many models eventually explode or decay to some fixed point (like a cycle or fixed value). This is a red flag that either the model is inadequate or training has failed you.

A simple dummy test for this would be training on something like a spin glass or Lorenz attractor, any kind of chaotic system really. Or just look along any interesting dimension of the data that you are using. A good model when recursively applied to itself will look very similar to the original signal in how it behaves regardless of phase.