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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.

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  • $\begingroup$ Hi: if there's a unit root, then the DGP implies that the variance is not constant ( the response is kind of a random walk ) and all the standard statistical assumptions that allow one to prove all the classical results no longer hold. I would either 1) read and understand the original dickey-fuller paper ( I think it was in the 70's ) or halbert white's blue book. In fact, I would recommend the latter because original papers are often succinct and don't provide the foundations for understanding. $\endgroup$ – mlofton Oct 2 at 2:19
  • $\begingroup$ I highly recommend White's book. It's thorough but also explains everything clearly or gives the reference, unlike a lot of books on asymptotics. amazon.com/… $\endgroup$ – mlofton Oct 2 at 2:22

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