Abstract :
Based on an idea of Granger ~1986, Oxford Bulletin of Economics and Statistics
48, 213–228!, we analyze a new vector autoregressive model defined from the
fractional lag operator 1 ~1 L!d+ We first derive conditions in terms of the
coefficients for the model to generate processes that are fractional of order zero+
We then show that if there is a unit root, the model generates a fractional process
Xt of order d, d 0, for which there are vectors b so that bʹXt is fractional of
order d b, 0 b 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, bʹXt is
fractional of order d b, and a linear combination of bʹXt and DbXt is fractional
of order d 2b+ The representations and conditions are analogous to the wellknown
conditions for I ~0!, I ~1!, and I ~2! variables+
