Recurrent boom-and-bust cycles are a salient feature of economic and financial history. Cycles found in the data are stochastic, often highly persistent, and span substantial fractions of the sample size. We refer to such cycles as "long". In this paper, we develop a novel approach to modeling cyclical behavior specifically designed to capture long cycles. We show that existing inferential procedures may produce misleading results in the presence of long cycles, and propose a new econometric procedure for the inference on the cycle length. Our procedure is asymptotically valid regardless of the cycle length. We apply our methodology to a set of macroeconomic and financial variables for the U.S. We find evidence of long stochastic cycles in the standard business cycle variables, as well as in credit and house prices. However, we rule out the presence of stochastic cycles in asset market data. Moreover, according to our result, financial cycles as characterized by credit and house prices tend to be twice as long as business cycles.

翻译：反复出现的繁荣-衰退周期是经济金融史的一个显著特征。数据中发现的周期具有随机性、高度持续性，且其长度占样本容量的相当大比例。我们称这类周期为"长期周期"。本文开发了一种专门用于捕捉长期周期的周期行为建模新方法。我们证明，在存在长期周期的情况下，现有推断程序可能产生误导性结果，并提出一种新的用于周期长度推断的计量经济学程序。该程序无论周期长度如何均具有渐近有效性。我们将该方法应用于美国的一系列宏观经济与金融变量。我们在标准商业周期变量以及信贷和房价中发现了长期随机周期的证据。然而，我们排除了资产市场数据中存在随机周期的可能性。此外，根据我们的研究结果，由信贷和房价表征的金融周期长度往往是商业周期的两倍。