Overview -- Methods for describing oscillations, fluctuations, and cycles in univariate series -- Constructing reference cycles with multivariate information -- Model-based rules for describing recurrent events -- Measuring recurrent event features in univariate data -- Measuring synchronization...

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...

1 Introduction -- 2 ‘Classical’ Techniques of Modelling Trends and Cycles -- 3 Stochastic Trends and Cycles -- 4 Filtering Economic Time Series -- 5 Nonlinear and Nonparametric Trend and Cycle Modelling -- 6 Multivariate Modelling of Trends and Cycles -- 7 Conclusions.