Nonlinear time series analysis of business cycles The business cycle has long been the focus of empirical economic research. Until recently statistical analysis of macroeconomic fluctuations was dominated by linear time series methods. Over the past 15 years however economists have increasingly applied tractable parametric nonlinear time series models to business cycle data; most prominent in this set of models are the classes of Threshold AutoRegressive (TAR) models Markov Switching AutoRegressive (MSAR) models and Smooth Transition AutoRegressive (STAR) models. In doing so several important questions have been addressed in the literature including: 1. Do out of sample (point interval density and turning point) forecasts obtained with nonlinear time series models dominate those generated with linear models 2. How should business cycles be dated and measured 3. What is the response of output and employment to oil price and monetary shocks 4. How does onetary policy respond to asymmetries over the business cycle 5. Are business cycles due more to permanent or to transitory negative shocks 6. Is the business cycle asymmetric and does it matter