The textbook is extremely confusing when it comes to this topic.
Under what circumstances do we have to readjust the regression coefficients in the mode in regards to serial correlationl? I am specifically confused on how this related to having a lagged dependent variable in the regression.
For AR, ARMA or MA models you can incur in model misspecification, so looking at serial correlation indicators (probably up to 30+ levels of lag differences) will tell us if the model requires adjustments. Those adjustments are very simple like adding or removing lagged dependent variables as explicators (i.e. independent variables).