Vector Autoregressive Models

A Vector Autoregressive (VAR) model is a fundamental tool in multivariate time series analysis. The concept is to extend the idea of autoregressive models, which explain a variable in terms of its own past values, into the multivariate case,where multiple interrelated time series are modeled together. A VAR model captures the linear interdependencies among multiple time series variables. That is, a VAR(p) model expresses each variable as a linear function of its own past values and the past values of all other variables: Each variable in the system is explained by its own past values (auto regression) and the past values of all other variables in the system

The steps in VAR analysis include defining date and time, stationary check, model estimation, lag order selection, model diagnostics, and forecasting.

Statistics
  • For each variable: Identifies the number of valid cases, measures the mean and standard deviation, and specifies the minimum and maximum values.
  • For each model: Assesses the parameter estimates (coefficients), standard error of coefficients, t-statistic, p-value (Sig.), lower and upper confidence intervals, covariance matrix of residuals, determinant of residual covariance matrix, correlation matrix of residuals, eigen values of residual correlation matrix, residual sum of squares, R square, Adjusted R square, MSE, RMSE, MAE, MAPE, Ljung-Box test for autocorrelation of residuals, and Jarque-Bera test for normality of residuals.
  • For goodness of fit: Calculates AIC, BIC, and HQIC for various lags.
  • Plots: Time series, ACF, residual plot for each variable, combined residual plot, residual ACF plot for each variable, fit values, and forecast.
Data Considerations
  • Endogenous variables must be scale. A minimum of 2 variables are required.
  • Exogenous variables can be scale or categorical. This is optional

Obtaining Vector Autoregressive Models

  1. VAR models are applicable only for time series data. Click Define date and time to generate date and time variables. See Define Dates for more information.
  2. Stationarity is essential for VAR modeling. Non-stationary series often require differencing or cointegration analysis.

    A stationary time series is one whose statistical properties such as mean, variance, and autocorrelation remain constant over time. Before you move to fit a VAR model, make sure that the time series is stationary.

    For non-stationary series, take the first difference of actual data and check for Stationary. Take the difference again and continue the procedure until the data attains stationarity.

    The Augmented Dickey-Fuller (ADF) test can be used for checking stationarity. ADF test is part of the extension procedure, STATS TSTESTS. After you install STATS TSTESTS, go to Analyze > Forcasting > Stationarity and Cointegration Tests. Select a variable and click Tests. Select Compute test (one variable) for Augmented Dickey-Fuller Test.. Run the test.

  3. After the stationary test, click Analyze > Forcasting > Mutivariate Time Series > Vector Autoregressive Models.
    Note: The fields highlighted in red are required. The Paste and OK buttons are enabled after you enter valid values in all required fields.
  4. Select the Endogenous and Exogenous variables where, Exogenous variables are optional.

  5. The optimal lag length must be chosen for better forecasting. This can be performed based on the selection by using the various goodness of fit criterion or information criterion: AIC (Akaike Information Criteria), BIC (Bayesian Information Criteria, or HQIC (Hannan Quin Information Criteria).

  6. Select the options from Statistics tab, Plots tab, Save tab, and Options tab.
  7. Click OK.

This procedure pastes VAR MODEL command syntax.