How to change the observation for the first lag in an AR(1) model? I run a simple AR(1) model in my analysis using ols:



ar.ols(df$y, order.max = 1))


However, I work with generations as my unit of analysis. Therefore, the first lag of y would be the observation of y at time t-30. How can I specify this in the AR(1) model in R?
The ar.ols() function in R defaults to order $10log_{10} (N)$.  This implies that, to catch the 30th time lag, you need at least 1000 observations. That seems like a lot, but bear in mind that you are then running OLS on 30 features (lags t-1 to t-30). All else equal, it is not clear why 30 is the magic number for you here, and you can't just drop the more recent lags as they may have the dominant effect.

Without knowing more about your study, it's hard to recommend further.  Intuitively, though, I would not expect to be using annualized data to perform generational analysis unless I were running OLS (not AR) and explicitly constructing a lagged column vector to use as an additional feature alongside contemporaneous features/controls.