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In this paper we derive (weak) consistency and the asymptotic distribution of pseudo maximum likelihood estimates for multiple frequency I(1) processes. By multiple frequency I(1) processes we denote processes with unit roots at arbitrary points on the unit circle with the integration orders corresponding to these unit roots all equal to 1. The parameters corresponding to the cointegrating spaces at the different unit roots are estimated super-consistently and have a mixture of Brownian motionsdoi:10.7892/boris.142913 fatcat:hfegaw66qna77inueomiptssci