Models for the analysis of alternative sources of growth in correlated stochastic variables

An approach to the analysis of multivariate time series is presented in which linear structural relationships among multiple stochastic variables are investigated. A number of alternative structural models are considered for the case of two stochastic variables. Each model represents a possible hypothesis concerning the relationship of growth in one variable to growth in the second. Both symmetric and asymmetric models are considered. Extensions of two of the models to three variables are illustrated by means of a numerical example. Implications of the models for the problem of detecting change in multivariate time series are discussed.This paper is based in part on a paper read at the Psychometric Society Meetings, Princeton, N. J., Mar. 30–31, 1972. The research was supported by the Committe on Basic Research in Education, National Academy of Sciences, Grant No. OEG-0-9-140396-4497(010), Project No. 9-0396.