This chapter looks at observed features of the cycle in a variety of time series. It sets out these features for the United States and a number of other countries, and then asks whether these features can be replicated by the use of a particular statistical model—a linear autoregression. For such linear models it is possible to broadly account for the observed features using moments of the series for growth rates, and this strategy is employed in the chapter. It then uses a particular nonlinear statistical model to see if it can match all the features, and further looks at two other nonlinear models first dealt with in Chapter 4. The chapter concludes with an examination of whether the binary indicators summarizing the recurrent states can be used in the context of standard multivariate methods such as vector autoregressions. This turns out not to be straightforward owing to the nature of the binary variables.