A fundamental issue that arises after fitting a regression model is that of testing the goodness of the fit. Our work brings together the power divergence family of goodness of fit tests and regression models for categorical time series. We show that under some reasonable assumptions, the asymptotic distribution of the power divergence family of goodness of fit tests converges to a normal random variable. This fact introduces a novel method for carrying out goodness of fit tests about a regression model for categorical time series. We couple the theory with some empirical results.