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

Soren Johansen

Econometric Theory, 2008, vol. 24, issue 3, 651-676

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 β so that β‼Xt is fractional of order d − b, 0

Date: 2008
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