I am pretty naive when it comes to time series modeling, but I think AR is expecting parameters for each series you are observing. If you want to use a single set of parameters for all observed series and do it in a single likelihood, then maybe something like this?
import aesara.tensor as at
with pm.Model(coords={"time": df.index.values, "series": [0, 1]}) as m:
rho = pm.Normal("rho")
init = pm.Normal.dist(shape=2)
sigma = pm.HalfNormal('sigma')
ar1 = pm.AR("ar1",
rho=at.stack([rho, rho]),
sigma=at.stack([sigma, sigma]),
init_dist=init,
observed=df[['res1', 'res2']].to_numpy().T,
dims=("series", "time")
)
Of course, you should also be able build 2 separate likelihoods, which should do the same thing, but then you wouldn’t have everything in one giant data structure with series as a dimension.