All economists say that they want to take their models to the data. But with incomplete and highly imperfect data, doing so is difficult and requires carefully matching the assumptions of the model with the statistical properties of the data. The cointegrated VAR (CVAR) offers a way of doing so. In this paper we outline a method for translating the assumptions underlying a DSGE model into a set of testable assumptions on a cointegrated VAR model and illustrate the ideas with the RBC model in Ireland (2004). Accounting for unit roots (near unit roots) in the model is shown to provide a powerful robustification of the statistical and economic inference about persistent and less persistent movements in the data. We propose that all basic assumptions underlying the theory model should be formulated as a set of testable hypotheses on the long-run structure of a CVAR model, a so called ‘theory consistent hypothetical scenario’. The advantage of such a scenario is that it forces us to formulate all testable implications of the basic hypotheses underlying a theory model. We demonstrate that most assumptions underlying the DSGE model and, hence, the RBC model are rejected when properly tested. Leaving the RBC model aside, we then report a structured CVAR analysis that summarizes the main features of the data in terms of long-run relations and common stochastic trends. We argue that structuring the data in this way offers a number of ‘sophisticated’ stylized facts that a theory model should replicate in order to claim empirical relevance.