Ok, so there are a number of ways in which a model can be misspecified (6 I believe) One of them is giving me some trouble. Misspecification #4: Using lagged dependant variable as independant variable. Huh? Isn’t that the definition of an autoregressive model? The definition of an AR model: “In autoregressive models, the dependant variable is regressed against one or more lagged values of itself.” Am I missing something? Can anyone help reconcile? Thanks

It would be a problem in normal regression. AR model is used to resolve the conditional hetroskedacity.

No ur not. Lagged dependent variables as independent variables can be non covariance stationary. That is where the problem comes in.

AR model uses lagged dependent variable as independent variable. If ARCH exists, there are ways to resolve.

Smarshy is asking if AR (time-series) model are all mis-specified.

Any model can be misspecified. In multiple regression, using lagged dependent as independent would create misspecification. But in time series, AR model uses lagged dependent as independent because we are trying to predict Y based on Y’s past behavior. In multiple regression we are trying to predict Y based on X’s behavior. So, using Y’s past behavior to predict Y’s future behavior is not correct in multiple regression. AR model is misspecified not simply because we use Y’s past behavior but for other reasons such as covariance instationary, serial correlation of Y’s past behavior.