Are linear models really unuseful to describe business cycle data?

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. The evidence we find does not support some descriptions because the presence of significant non-linearities is observed for 2/3 of the countries only. Linear models cannot be simply dismissed as they are frequently useful. Contrarily to common knowledge, nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. This finding is particularly surprising for the U.S. case. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this is marginal to our study, based on indirectmethods only and can hardly be invoked to support nonlinearity in classical business cycles.