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Title: A parameterization of MFI(1) and I(2) processes: Structure theory with an eye to hypothesis testing Authors:  Dietmar Bauer - University Bielefeld (Germany) [presenting]
Lukas Matuschek - Technical University Dortmund (Germany)
Patrick de Matos Ribeiro - Technical University Dortmund (Germany)
Martin Wagner - University of Klagenfurt (Austria)
Abstract: Important properties of a parameterization of state space models for unit root processes for the multiple frequency I(1) and I(2) cases are discussed. Given that formulating and estimating hypotheses on the cointegrating spaces is of particular importance, special emphasis is placed on describing the implementation of a variety of relevant hypotheses tests. A continuous parameterization necessarily partitions the set of all systems of a given minimal order into pieces, with the pieces described here by multi-indices (e.g., the unit root structure, Kronecker indices). The relation between the different pieces are discussed in detail, and it is shown, similar to the stationary case, that some pieces are at the boundary of other pieces. This structural information is of vital importance for parameter estimation and hypothesis testing in particular cointegrating ranks in, e.g., pseudo maximum likelihood estimation.