# Estimating AR process for Logistic Regression

I'm fitting a time-series model with independent $X$ variables coded as months of the year (so there are 12 of them) and the dependent $y$ variable is some proportion, bounded between 0 and 1. As a result, I'm using a GLM with logit link function. The fit is pretty good.

I notice, however, that my residuals are autocorrelated (and this is corroborated by a DW statistic close to 0).

I'm able to fit an AR(1) model to the residuals and I'd like to see what the impact has on my GLM-fitted model. However, when my $X$ variables are categorical, what does it mean to add an AR(1) term? Can I just do the same thing as if they were continuous, i.e. $X_{t}$ = $\phi$$X_{t-1}$? It seems odd since my $X$'s take on values of 1 or 0.