I have a dataset where I have the number of patients who were admitted due to a condition in a area in a specific day. To predict which are the ambient variables that affect the number I have fitted a poisson model, where I included multiple environmental variables (temperature, pressure, loudness …). I also included in the model the sine and cosine of 180, 90, 360 days for seasonality, and the day of the week as constant effects.
For each of the environmental variables, I included all of them in the model, and in case some of them are not significant, I removed them and included the +1 lag of them
I also want to adjust for the autoregressive component of the dependent variable. The partial autocorrelation of the variable indicates that lags 1, 2, 3, 5, 6, 8 and 9 are significant.