In this tutorial, you will learn how to estimate Vector Autoregression (VAR) models, one of the most widely used tools in macroeconomics and time series analysis. Their popularity stems largely from the work of Christopher Sims, who introduced VAR models in 1980 as an alternative to large-scale structural models composed of multiple equations and strong theoretical assumptions. These assumptions were often difficult to justify or specify correctly. Sims’ key idea was to “let the data speak for itself.”

VAR models are multivariate time series models in which each endogenous variable is explained by its own past values (lags) as well as the past values of all other variables in the system. This makes them flexible and relatively straightforward to implement.

For illustrative purposes and to motivate the analysis, this tutorial replicates key ideas from James Stock and Mark Watson (2001), who evaluate the empirical performance of VAR models in macroeconomic applications.

By the end of this tutorial, you will have learned:

• What VAR models are

• The mathematical representation of VAR models

• How to estimate VAR models in R

• How to select the appropriate lag length

• How to compute impulse response functions (IRFs)

• Identification strategies: Cholesky decomposition and recursive ordering

• How to perform forecast error variance decomposition (FEVD)

• How to conduct Granger causality tests

• How to produce forecasts using VAR models