# Do "Mixed Effects Time Series Models" Exist?

Suppose I have the number weekly of hospital visits in a certain ZIP code (10 years of data) - this ZIP code has a small population in general and as a result, not that many people visit the hospital within this ZIP code. If I were to fit a basic time series model (e.g. ARIMA) to this data, I might run into some difficulties because I don't have enough data.

Suppose I also have the weekly number of hospital visits at the State Level and at the Country Level. Additionally, at the yearly level - I have information on the total population and the average income of all residents within the ZIP code, the State and the Country. Furthermore, I also have information on whether a given year the President of the Country and the State Governor was a Democrat or Republican, and indicator variable for Pre-Covid/Post-Covid.

Based on this information, I had the following ideas:

• Suppose I were to use a VAR Model - in which the weekly hospital visits in the ZIP code are modelled using weekly hospital visits from the State Level and the Country Level. The idea being that perhaps I could "statistically pool" relevant and related information to improve my weekly estimates. By doing this, am I basically creating a "Mixed Effects Time Series Model"?
• On top of what I just described - suppose I decide to add information to the above model on Covid and Democrat/Republican, thus making the model similar to an ARMAX/ARIMAX. From a conceptual point-of-view, is this also similar to a "Mixed Effects Time Series Model"?

In general, I am not sure if these approaches that I have described above "statistically valid approaches" or if they fundamentally flawed and likely will result in model violations.

Thanks!

• You can usually make a mixed-effects model by replacing a parameter with a fixed effect and one-or-more random effects. VAR is not an exception. Feb 2, 2023 at 5:05
• Sure, if you just apply the definition of these things then it's straightforward. You might be thinking of a single time series, in which case it would be unlikely to do any good mixed modeling. Feb 2, 2023 at 5:28