Order selection statistical test for nonstationary AR models

A new statistical test for selecting the order of a nonstationary AR modelyk is presented based on the predictive least-squares principle. This test is of the same order as the accumulated cost function _n=_k=1ⁿ(_k^*–_k)²;i.e., ^* wherey_k^* is the predictive least-square estimate. It is constructed to show how many times the integrated AR processy_k is differenced in order to obtain a stationary AR process given that the exact order of the process is unknown.