When we have several time series, we need to take into account the interdependence between them. The VAR model is a very useful starting point in the analysis of the interrelationships between the different time series. The VAR is just a multiple time-series generalization of the AR model. The VAR model is easy to estimate because we can use the OLS method. The VAR is commonly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random disturbances on the system of variables. where yt is a k vector of endogenous variables, xt is a d vector of exogenous variables, A1,…, Ap and Ī² are matrices of coefficients to be estimated, and Īµt is a vector of innovations that may be contemporaneously correlated with each other but are uncorrelated with their own lagged values and uncorrelated with all of the right-hand side variables. In practice, since we are not considering any moving average errors, the autoregressions would probably have to
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