Abstract
The paper sets out some simple statistical models and shows that they are capable of generating the observed characteristics of classical cycles in three countries, Australia, the United Kingdom, and the United States. Both analytical and simulation work is used for this purpose. These models emphasize the fact that to generate a realistic business cycle requires some deterministic trend growth, near unit root behaviour in the deterministically detrended data, and innovations of a certain magnitude. With this information we examine some popular models of the cycle, asking how they produce these features, and then explore the implications of the analysis for economic policy.

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