Abstract:
Based on an idea of Granger (1986, Oxford Bulletin of Economics and Statistics 48, 213 (1 so that Xt is fractional of order d d. We find a representation of the solution that demonstrates the fractional properties. Finally we suggest a model that allows for a polynomial fractional vector, that is, the process Xt is fractional of order d, Xt is fractional of order d bXt is fractional of order d 2b. The representations and conditions are analogous to the well-known conditions for I(0), I(1), and I(2) variables.
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