This paper proposes a new modeling framework capturing both the long-run and the cyclical components of a time series. As an illustration, we apply it to four US macro series, namely, annual and quarterly real gross domestic product (GDP) and GDP per capita. The results indicate that the behavior of US GDP can be captured accurately by a model incorporating both stochastic trends and stochastic cycles that allows for some degree of persistence in the data. Both appear to be mean reverting, although the stochastic trend is nonstationary, while the cyclical component is stationary, with cycles repeating themselves every 6–10 years.

中文翻译：

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宏观系列的趋势和周期：以美国实际 GDP 为例

本文提出了一种新的建模框架，可以同时捕捉时间序列的长期和周期性成分。作为说明，我们将其应用于四个美国宏观系列，即年度和季度实际国内生产总值（GDP）和人均 GDP。结果表明，美国 GDP 的行为可以通过包含随机趋势和随机周期的模型准确捕获，该模型允许数据具有一定程度的持久性。两者似乎都是均值回归，尽管随机趋势是非平稳的，而周期性成分是平稳的，周期每 6-10 年重复一次。