I have constructed a linear time series regression model and estimated the parameters by applying OLS. I now want to test wether the assumptions for proper large sample inference (asymptotic Gauß Markov assumptions) are fulfilled.
Now, I am not sure how to test wether the residuals are autocorrelated or not. Since my model contains lagged dependent variables I can not use the Durbin-Watson test (since my independent variables are not strictly exogenous). Following Wooldridge I decided to apply the Breusch-Godfrey test. But the residuals are heteroscedastic, which I tested for via applying the Bresuch-Pagan test.
Wooldridge says that in the case of heteroscedasticity, one can not apply the usual Breusch-Godfrey test. How can I test for autocorrelation in the presence of heteroscedasticity? Is there any robust method? If that is of any interest - I am using R, so it would be helpful if there would be an implementation of the method (if there is one) in R.
EDIT: I have found a quite interesting paper that proposes a method of dealing with the topic: The modified Breusch-Godfrey test. Link: http://www.naun.org/main/NAUN/mcs/17-542.pdf.
Yet, I did not find any practical implementations of this test. As I am (just) an undergrad student, my possibilities regarding implementing such methods on my own are rather limited. So I am still looking for a general approach/test or method. (And I assume there has to to be a method, because the problem I am having strikes me as a rather common one.) Thank you!