It says one of the model misspecifications is “using a lagged dependent variable as independent variable”, but isn’t that what you’re doing with autoregression?

Are they talking about multiple regressions?

Yes, but if you see a model using a lagged value as the independent variable, how do you know if its correctly specified as an autoregressive model or incorrectly specified as a multiple regression?

I would think if you have a dependent variables like industry sales with a group of independent variables like GDP growth, level of interest rates, and industry sales from last quarter I would think that the model is misspecified because its grouping independent variables with a lagged variable of the dependent variable. I am no quant stud though.

It’s not a problem if the error terms are not serially correlated.