The business cycle is a complex phenomenon which attracts both scientific and public interest. But what are the defining characteristics of the business cycle? Is the business cycle asymmetric or non-linear? What can be said about the occurrence of turning points over time? This book gives an overview over the most popular non-linear time series models and their main characteristics and possible application to business cycle time series. The basic ideas of testing, estimation and forecasting with many references for further reading will be presented. Furthermore the book outlines concepts for detecting non-linearity in a time series. By fitting and accepting a special model, new insights in understanding the structure of a time series can be gained. As an empirical application and illustration we apply the presented models to the three famous Ifo indicators: the Business Assessment, the Business Expectations and the Business Climate. The book can be understood as a starting point for own applications to empirical business cycle analysis. It addresses financial analysts, researchers, and anyone else who is interested in business cycle analysis and non-linear time series concepts.