Vector Auto-Regressions or VARs are used in time series analyses when there may be inter-dependencies or relationships among multiple time series. For example, we may want to understand the relationship between GDP, current account balance, and inflation rates. Running a normal OLS regression would be inappropriate as each variable affects the other variables; OLS estimates would have an endogeneity problem or the estimates would be biased. In such scenarios, we use VAR methods.
Recently, I was working on some time series data that had the issues of reverse causality. As a result, I had to use a VAR model to get orthogonalized impulse response functions (OIRFs) in order to understand the relationship between variables. In the attached presentation, I describe the theory behind this orthogonalization as well as the steps to generate OIRFs on STATA.
To check the presentation, please click on this link