Identification of Colinear and Cointegrated Multivariable Systems Using Canonical Variate Analysis

Abstract

This paper addresses the problem of identification of a multivariate system where the output time series may be colinear and perhaps integrating processes. Such processes can occur when numerous measurement series are available for observing basically the same process with slight changes. Examples include financial series from the same economic sector, high dimensional series in the measurement of sheet forming processes such as sheet aluminum or paper machines, and highly instrumented vibrating structures. Basically, some of the measurements are providing information already contained in other measurements. By explicitly dealing with the possible rank deficiency of the measurements, a reduced rank process can be determined that can have far fewer parameters to estimate. Since modeling accuracy as measured by variance is proportional to the number of estimated parameters, the resulting models can be considerably more accurate. Maximum likelihood tests of hypotheses are constructed to determine the best reduced rank structure by optimal statistical tests.