I have been confused with these two methodologies when doing regression.
Let's say I have a dependent variable (DV), which is auto-correlated. When I regress the dependent variable on a number of independent variables (IV), most likely, the residuals are auto-correlated as well.
After doing some search on the internet, my understanding is that, when such a situation emerges, roughly speaking, the methodologies to handle this fall into two categories:
Including lagged DV as independent variables
Treating the residuals as an AR process. It seems that there are a number of ways to do this:
a. Use Heteroskedasticity and Autocorrelation Consistent (HAC) robust standard errors while leaving the model specification unchanged.
b. Something like the Cochrane-Orcutt Procedure.
c. Using Maximum Likelihood Estimate assuming a ARIMA(p,d,q) structure for the residuals.
I would like to know if my above understanding is correct. If so, then how could one make a decision about which approach to use? Last, when using the first methodology, i.e., including lagged DV as independent variables, can Ordinary Least Squares (OLS) still be used to estimate the parameters and is OLS still consistent, unbiased, etc.?