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Structural Equation Modeling of Multivariate Time Series.

Stephen H C du Toit1, Michael W Browne2

  • 1a Scientific Software International.

Multivariate Behavioral Research
|January 29, 2016
PubMed
Summary
This summary is machine-generated.

This study derives the covariance structure for vector autoregressive moving-average (VARMA) processes, offering a new formula compatible with structural equation modeling. This enables fitting VARMA models using standard software like LISREL.

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Vector Autoregressive Moving-Average (VARMA) models are crucial for analyzing multivariate time series data.
  • Existing methods for deriving VARMA covariance structures have limitations.
  • Compatibility with structural equation modeling (SEM) is desirable for broader application.

Purpose of the Study:

  • To derive a novel covariance structure for stationary VARMA processes.
  • To ensure the derived structure is compatible with current structural equation methodology.
  • To demonstrate the impact of initial conditions on the covariance matrix.

Main Methods:

  • Derivation of the covariance structure for VARMA processes.
  • Comparison with existing covariance function expressions.
  • Utilizing structural equation modeling (SEM) principles for model fitting.
  • Analysis of assumptions regarding the process before the first observation.

Main Results:

  • A new expression for the covariance structure of stationary VARMA processes is presented.
  • The derived structure is shown to be compatible with SEM.
  • The influence of initial state assumptions on the reproduced covariance matrix is quantified.

Conclusions:

  • The novel covariance structure facilitates the application of SEM to VARMA models.
  • Standard SEM software can be employed for fitting these models.
  • Understanding initial condition assumptions is vital for accurate VARMA model analysis.