In this paper it is shown that several models for a bivariate nonstationary quarterly time series are nested in a vector autoregression with cointegration restrictions for the eight annual series of quarterly observations. Or, the Granger Representation Theorem is extended to incorporate, e.g., seasonal and periodic cointegration.

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Keywords cointegration, periodic models, seasonality
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Journal Econometric Reviews
Franses, Ph.H.B.F. (1995). A vector of quarters representation for bivariate time series. Econometric Reviews, 55–63. doi:10.1080/07474939508800303