The residual of a seasonal_decompose (from python's statsmodels) yields the following ACF and PACF plots
The sampling frequency of the time series is hourly, so the ACF plot hints at daily (24 hour) seasonality, which is leaking from the seasonal_decomposition (I haven't been able to find a decomposition that doesn't leak some of this seasonality).
Anyway, I need to move forward and model this residual. However the SARIMAs I have so far used with orders (3,0,0)(0,0,4,24) haven't been doing very well. I see as a rule of thumb people take the significant ACF peaks to stand for MA orders, and significant PACF peaks to stand for AR orders, but I don't know the theoretical motivation behind that rule. Do you have any suggestions for how to capture this signal? It is normally distributed.