Vector autoregression

A structural VAR is simply one where the errors are uncorrelated with one another across the various included time series.

Dealing with nonstationarity

”VAR models are usually guided by theory and are dynamic in nature, so you do not have to worry about the nonstationarity.” (Source)
“There is an issue of whether the variables in a VAR need to be stationary. Sims (1980) and Sims, Stock and Watson (1990) recommend against differencing even if the variables contain a unit root. They argued that the goal of a VAR analysis is to determine the interrelationships among the variables, not to determine the parameter estimates. The main argument against differencing is that it “throws away” information concerning the comovements in the data (such as the possibility of cointegrating relationships). Similary, it is argued that the data need not be detrended. In a VAR, a trending variable will be well approximated by a unit root plus drift. However, majority view is that the form of variables in the VAR should mimic the true data-generating process. This is particularly true if the aim is to estimate a structural model.” (Source)