Autoregression with multiple factors

Question

I am not sure if this is the right place to ask this question. Anyway, I am working on a Forecasting using spending data. Using autoregression, I am able to predict the following number decently well but I would like to improve this. I have two other factors that don't predict nearly as well as the lagged factor but could still be useful in the model.

My question is this: would it be valid to include those factors in the model even though I am using a lagged version of the predictor? Does an autoregression imply that the only factor to be used is the lagged version of the predicted value?

I can't show the data as it is sensitive and my question is more about how autoregression and forecasting work in general.

Thanks for any help.