经济周期的阶段划分属于聚类问题中特殊的类型，需要对有序的时间序列样本进行分割，而经济周期的有序阶段划分则是研究经济周期相关问题的基础工作。文中构建以国内生产总值（gross domestic product， GDP）和居民消费价格指数（consumer price index， CPI）为基础数据的经济发展指标向量，提出针对经济周期阶段划分的有序样本最优分割算法，并分别选取美国1948年第三季度至2008年第二季度和日本1971年第三季度至2008年第二季度的数据为样本，动态分析算法的精度趋势和最优分割效果,为经济周期的阶段划分提供一种高效、简洁的算法。

Clustering often plays a foundational role in solving practical problems. The partitioning of economic cycles into stages represents a specialized clustering challenge, requiring the segmentation of sequential time series samples. The orderly division of economic cycle stages is fundamental to studying problems related to economic fluctuations. This paper presents an economic development indicator vector based on data from the gross domestic product(GDP)and consumer price index of residents(CPI). It introduces an optimal segmentation algorithm for ordered samples to partition economic cycle stages and analyzes the algorithm’s accuracy trend and optimal segmentation effect using sample data from the 3rd quarter of 1948 to the 2nd quarter of 2008 of the United States, and from the 3rd quarter of 1971 to the 2nd quarter of 2008 of Japan. The study offers an efficient and concise algorithm for delineating economic cycle stages.

F224.3

国家自然科学基金项目（71963037）；云南省哲学社会科学创新团队（2023CX05）。