A REPRESENTATION THEORY FOR A CLASS OF VECTOR AUTOREGRESSIVE MODELS FOR FRACTIONAL PROCESSES

SØren Johansen
2008 Econometric Theory  
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 the
more » ... demonstrates the fractional properties. Finally we suggest a model that allows for a polynomial fractional vector, that is, the process X t is fractional of order d; 0 X t is fractional of order d b and a linear combination of 0 X t and b X t 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.
doi:10.1017/s0266466608080274 fatcat:kxtjy5hlyfc7rnnvr5ydkifq7e