A REPRESENTATION THEORY FOR POLYNOMIAL COFRACTIONALITY IN VECTOR AUTOREGRESSIVE MODELS

We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008, <italic>Econometric Theory</italic> 24, 651–676). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given, and it is shown under which condition the solution of the model is fractional of order <italic>d</italic> and displays cofractional relations of order <italic>d</italic> − <italic>b</italic> and polynomial cofractional relations of order <italic>d</italic> − 2<italic>b</italic>,…, <italic>d</italic> − <italic>cb</italic> ≥ 0 for integer <italic>c</italic>; the cofractional relations and the corresponding moving average representation are characterized in terms of the autoregressive coefficients by the same algorithm. For <italic>c</italic> = 1 and <italic>c</italic> = 2 we find the results of Johansen (2008).