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Based on an idea of Granger (1986), we analyse a new vector autoregressive model de...ned from the fractional lag operator 1 (1 L) d : We ...rst derive conditions in terms of the coe¢ cients for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X t of order d; for which there are vectors so that 0 X t is fractional of order d b: We ...nd a representation of the solution which demonstrates thedoi:10.1017/s0266466608080274 fatcat:kxtjy5hlyfc7rnnvr5ydkifq7e