Time series models are a common approach in economic and econometric analysis. A special case are Vector Error Correction models where several economic variables are assumed to depend on their own and each other's recent developments. While they facilitate economically sound modeling, their actual application is often hampered by technical difficulties: Finding the optimal parameter values is usually based on maximizing some likelihood function or ``information criterion'' with no closed-form solution. Even more importantly, the number of parameters to estimate increases quickly when allowing for more lags, i.e., including past observations --- which is highly desirable, e.g., when seasonalities, delayed reactions, or long memory need to be catered for. In this case, it is desirable to keep the model still as parsimonious as possible to avoid over-fitting. Ideally, one can ``cherry-pick'' the parameters which one does and doesn't want to include; this, however, makes parameter estimation even harder as it adds challenging combinatorial problems. In this paper, we investigate how Differential Evolution (DE), a nature-inspired search heuristic, can solve the parameter selection and estimation problem. The empirical part considers data for the US, Euro-Area and Switzerland and compares different model selection criteria. Results emphasize the importance of careful modeling and reliable estimation methods.