Multivariate time series analysis is an extension of univariate time series analysis to a system of response variables for studying their dynamic relationship. To investigate the interactions and comovements of the response series, you can include lags of all response variables in each equation in the system.
To begin a multivariate time series analysis, test your response series for cointegration. If the response series do not exhibit cointegration, create a vector autoregression (VAR) model for the series. Econometrics Toolbox™ supports frequentist and Bayesian VAR analysis tools. If the response series exhibit cointegration, create a vector error-correction (VEC) model for the series. For more details, see Vector Autoregression (VAR) Models.