Department of Economics and Business Economics

On the identification of fractionally cointegrated VAR models with the F(d) condition

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This paper discusses identification problems in the fractionally cointegrated system of Johansen (2008) and Johansen and Nielsen (2012). It is shown that several equivalent reparametrizations of the model associated with different fractional integration and cointegration parameters may exist for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d) condition. The paper also illustrates the indeterminacy between the cointegration rank and the lag-length. It is also proved that the model with rank zero and k lags may be an equivalent reparametrization of the model with full rank and k−1 lags. This precludes the possibility to test for the cointegration rank unless a proper restriction on the fractional integration parameter is imposed.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages33
Publication statusPublished - 9 Jun 2014
SeriesCREATES Research Papers
Number2014-43

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