We develop a method for directly modeling cointegrated multivariate time series that are observed in mixed frequencies. We regard lower-frequency data as regularly (or irregularly) missing and treat them with higher-frequency data by adopting a state-space model. This utilizes the structure of...

An extension of Gaussian reduced rank estimation of Ahn and Reinsel (Journal of Econometrics, Vol. 62, pp. 317-350, 1994) to seasonal periods other than four is presented. Simple adjustments for estimation that are necessary because of complex-valued seasonal unit roots are presented in detail...

We investigate the effects of the misspecification of cointegrating ranks at other frequencies on the inference of seasonal cointegration at the frequency of interest such as test for cointegrating rank and estimation of cointegrating vector. Earlier studies mostly focused on a single frequency...