Forecasting multivariate time series data using VAR

In this recipe, you will explore the Vector Autoregressive (VAR) model for working with multivariate time series. In Chapter 10, Building Univariate Time Series Models Using Statistical Methods, we discussed AR, MA, ARIMA, and SARIMA as examples of univariate one-directional models. VAR, on the other hand, is bi-directional and multivariate.

VAR versus AR Models

You can think of a VAR of order p, or VAR(P), as a generalization of the univariate AR(p) mode for working with multiple time series. Multiple time series are represented as a vector, hence the name vector autoregression. A VAR of lag one can be written as VAR(1) across two or more variables.

There are other forms of multivariate time series models, including Vector Moving Average (VMA), Vector Autoregressive Moving Average (VARMA), and Vector Autoregressive Integrated Moving Average (VARIMA), that generalize other univariate models. In practice, you will find that...