A Distance Measure between Cointegration Spaces

by Rolf Larsson & Mattias Villani

Research Report 1999:3

 Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden


Abstract. A distinguishing feature of cointegration models, and many other multivariate models, is that only spaces spanned by parameter vectors are identified. We point out that traditional distance measures, such as the Euclidean measure, are not reasonable to use when measuring distances between spaces. This point has been either missed or ignored in many simulation studies where inappropriate distance measures have been used. We propose a simple measure based on the idea that the space spanned by the orthogonal complement of a matrix lies as far away as possible from the space spanned by the matrix itself. Several properties of this new measure are derived.

Keywords: Cointegration; Distance measure; Simulation studies.

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Last update: 1999-10-27/CE