Inspired by the paper by Guzman and Stiglitz (2020, ‘Towards a dynamic disequilibrium theory with randomness,’ NBER Working Paper 27453), this article shows that cointegrated VAR (CVAR) analyses have for many years provided empirical underpinnings for most of the topics discussed in that paper. The CVAR takes the nonstationarity of economic data seriously; it allows explicitly for complex adjustment dynamics in the short run and the long run; it is able to describe self-reinforcing feedback mechanisms leading to multiple equilibria; it is able to handle extraordinary shocks to the system whether they are exogenously or endogenously induced; and it is able to accommodate sizeable crisis periods such as the Great Recession. The article discusses these issues and many more from a methodological, econometric, and empirical point of view and illustrates the ideas with an application to the Phillips curve with a Phelpsian natural rate based on US data.