A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes
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 )null . 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 X null of order d , d > 0, for which there are vectors β so that β‼ Xnull 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 X null is fractional of order d , β‼ Xnull is fractional of order d − b , and a linear combination of β‼ Xnull and Δ null Xnull is fractional of order d − 2 b. The representations and conditions are analogous to the well-known conditions for I (0), I (1), and I (2) variables.
Volume (Year): 24 (2008)
Issue (Month): 03 (June)
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