In this paper we propose a time-varying parameter (TVP) vector error correction model (VECM) with heteroskedastic disturbances. We propose tools to carry out dynamic model specification in an automatic fashion. This involves using global–local priors and postprocessing the parameters to achieve truly sparse solutions. Depending on the respective set of coefficients, we achieve this by minimizing auxiliary loss functions. Our two-step approach limits overfitting and reduces parameter estimation uncertainty. We apply this framework to modeling European electricity prices. When considering daily electricity prices for different markets jointly, our model highlights the importance of explicitly addressing cointegration and nonlinearities. In a forecasting exercise focusing on hourly prices for Germany, our approach yields competitive metrics of predictive accuracy.