An important aspect of empirical research based on the vector autoregressive (VAR) model is the choice of the lag order, since all inferences in this model depend on the correct model specification. There have been many studies on how to select the lag order of a nonstationary VAR model subject to cointegration restrictions. In this work, we consider an additional weak-form (WF) restriction of common cyclical features in the model to analyze the appropriate way to select the correct lag order. We use two methodologies: the traditional information criteria (AIC, HQ and SC) and an alternative criterion (IC(p,s)) that selects the lag order p and the rank structure s due to the WF restriction. We use a Monte Carlo simulation in the analysis. The results indicate that the cost of ignoring additional WF restrictions in vector autoregressive modeling can be high, especially when the SC criterion is used.