Significant nonlinearities are found in several cyclical components macroeconomic time series across countries. Standard equilibrium models of business cycles successfully explain most first and second moments of these time series. Nevertheless, this paper shows that a model of this class cannot replicate nonlinear features of the data. Applying the Efficient Method of Moments (Gallant and Tauchen, 1996, 2000) methodology to build an algorithm that searches over the models parameter space establishes the parameterization that best allows replication of all statistical properties of the data. The results show that this parameterization captures nonlinearities in investment but fails to account for observed properties of consumption.