I feel it is useful to understand the consequence of violating the assumptions of a model. I check a couple textbooks, but most I can get about the consequence of fitting time series with unit root is that "traditional statistical theory do not apply to unit root process, such as law of large number and central limit theory".
I would like to understand a bit more. If I fit the data using AR model wihtout differencings, what are the impacts on unbiasness, consistency or prediction MSE. And why? Could anyone help to provide some more details?
Thank you in advance.