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.
- Cointegration Analysis
Engle-Granger cointegration test, and Johansen cointegration and constraint tests
- Vector Autoregression Models
Stationary multivariate linear models including exogenous predictor variables
- Vector Error-Correction Models
Multivariate linear models including cointegrating relations and exogenous predictor variables
- Bayesian Vector Autoregression Models
Posterior estimation and simulation using a variety of prior models for VARX model coefficients and innovations covariance matrix