By locating the running maxima and minima of a time series, and measuring the current deviation from them, it is possible to generate processes that are relevant for the analysis of the business cycle and for characterizing bull and bear phases in financial markets. First, the measurement of the time distance from the running peak originates a first-order Markov chain, whose characteristics can be used for testing time-reversibility of economic dynamics and specific types of asymmetries in financial markets. Second, the gap processes can be combined to provide a non-parametric measure of the growth cycle. The article derives the time series properties of the gap process and other related processes that arise from the same measurement context, and proposes new non-parametric tests of time-reversibility and new measures of the output gap.

中文翻译：

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经济时间序列的峰值、间隙和时间可逆性

通过定位时间序列的运行最大值和最小值，并测量当前与它们的偏差，可以生成与商业周期分析和金融市场牛市和熊市特征相关的流程。首先，测量与运行峰值的时间距离产生一阶马尔可夫链，其特性可用于测试经济动态的时间可逆性和金融市场中特定类型的不对称性。其次，可以组合间隙过程以提供生长周期的非参数测量。文章推导了同一测量背景下出现的缺口过程和其他相关过程的时间序列属性，并提出了新的时间可逆性非参数检验和输出缺口的新测度。