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My talk is based on an invited lecture given at the New Zealand Econometrics Study Group Meeting, which was held in March, 2007 at Auckland University in honor of Professor P.C.B. Phillips. The work of Professor Phillips, even if it is focused on the area of linear nonstationary models, is enormous. So it is hard for me to explore the whole of his work in this talk. I take up only a few results of his work, which I discuss and, hopefully extend.