In this paper we pursue an approach based on economic theory to illustrate possible shortcomings of widely-used detrending methods. Wenanalyze a simple model of economic growth and business cycles in which investment and technical progress are stochastic. The Hodrick-Prescottnand the Baxter-King filter are shown to detect spurious business cycles which are not related to actual cycles in the model. Our results cast doubts on the validity of commonly-accepted stylized business cycle facts. We also discuss the relation of business-cycle dating based on indicators of economic activity, as e.g. applied by the NBER, and the detrending results.