Structural Equation Modeling of Multivariate Time Series

Abstract

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be employed to fit the model. Particular attention is given to assumptions concerning the process before the first observation. An application to a repeated time series is used to demonstrate the effect of these assumptions on the structure of the reproduced covariance matrix.