A beta distribution is bound between zero and one – are you sure that’s what you want?
The easiest solution is to log your data, and model the log process as normal (pun intended). If you really don’t want to do that, you will need to make a custom AR(1) with non-normal innovations. You can follow this example notebook for the basics on how to make a custom time series distribution, and just swap out the normal innovations inside the ar_step function with something that will respect your non-negativity constraint, e.g. lognormal.