Abstract This paper is motivated by the fact that the standard deviation of cyclical TFP derived from the standard approach under the stochastic trend is not even close to the real-world data. The main part of the paper devotes to developing a new method to apply geometric Brownian motion to characterize TFP in continuous time and converting it to an estimated process of random walk with drift. As a result, the drift estimate together with the lagged TFP in the random walk process are the stochastic trend of TFP and the stochastic error term in the random walk with drift process is the cyclical component of TFP. I then have two findings: the first one is that the standard deviation of cyclical TFP derived from the new approach is much closer to the real-world data; the second one is that stochastic trend of TFP can be decomposed into three parts: an initial value, a deterministic trend, and a term involved with Weiner process. Moreover, this paper argues that, by recalculating the business cycle statistics based on a rational expectations model, if we remeasure the stochastic trend and cyclical component of TFP using the new approach, then the ability of real business cycle model to mimic real-world economic fluctuations will be significantly improved.

中文翻译：

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重新测量和分解商业周期中的随机趋势

摘要 本文的动机是这样一个事实，即随机趋势下的标准方法得出的周期性 TFP 的标准偏差甚至不接近现实世界的数据。论文的主要部分致力于开发一种新方法，应用几何布朗运动来表征连续时间的 TFP，并将其转换为具有漂移的随机游走的估计过程。因此，随机游走过程中的漂移估计与滞后的 TFP 一起是 TFP 的随机趋势，随漂移过程中的随机误差项是 TFP 的循环分量。然后我有两个发现：第一个是新方法得出的周期性 TFP 的标准偏差更接近现实世界的数据；第二个是TFP的随机趋势可以分解为三个部分：初始值、确定性趋势和与韦纳过程相关的术语。此外，本文认为，通过基于理性预期模型重新计算商业周期统计数据，如果我们使用新方法重新衡量 TFP 的随机趋势和周期性成分，那么真实商业周期模型模拟现实世界经济的能力波动将得到明显改善。