Vector Error Correction and Vector Autoregressive Models: Introduction to Macroeconometrics
The vector autoregression model is a general framework used to describe the dynamic interrelationship between stationary variables. So, the first step in your analysis should be to determine whether the levels of your data are stationary. If not, take the first differences of your data and try again. Usually, if the levels (or log-levels) of your time-series are not stationary, the first differences will be.
If the time-series are not stationary then the VAR framework needs to be modified to allow consistent estimation of the relationships among the series. The vector error correction model (VECM) is just a special case of the VAR for variables that are stationary in their differences (i. e., I(1)). The VECM can also take into account any cointegrating relationships among the variables.