I am creating two models, where the fitted values of one SARIMAX type model are used as an exogenous predictor for a second dynamic regression model. I want to understand what assumptions of the gauss markov theorems or any other relevant theorems I am violating to do this. I am doing this process, because if I model the predictors based upon their passed lagged and seasonal lagged values, it appears to be a better way to forecast out future values of these predictors, which I need to forecast the dependent variable in the dynamic regression model. Using detailed diagnostics per Pankratz is not what I can afford to do in my situation, I need to create more than a 100 different models within a for loop, using the same two tiered model frame work. I want to be aware of the type of biases, issues or best practices related to the tasks described above. I checked for similar questions on crossvalidated, the most similar ones do not have answers.