标题： 非参数趋势曲线的多尺度比较 显示英文标题

标题： Multiscale Comparison of Nonparametric Trend Curves

摘要： 我们开发了新的计量经济学方法，用于比较非参数时间趋势。 在许多应用中，实践者感兴趣的是观察到的时间序列是否都有相同的时间趋势。 此外，他们通常想知道哪些趋势不同以及在哪些时间区间内它们不同。 我们设计了一个多尺度检验，以正式解决这些问题。 具体而言，我们开发了一种检验方法，可以对哪些时间趋势不同以及它们在哪些时间区间内不同做出严格的置信陈述。 基于我们的多尺度检验，我们进一步开发了一种聚类算法，可以将观察到的时间序列聚类为具有相同趋势的组。 我们推导了检验和聚类方法的渐近理论。 该理论通过一个模拟研究以及对国内生产总值增长数据和房屋定价数据的两个应用得到了补充。 显示英文摘要

摘要： We develop new econometric methods for the comparison of nonparametric time trends. In many applications, practitioners are interested in whether the observed time series all have the same time trend. Moreover, they would often like to know which trends are different and in which time intervals they differ. We design a multiscale test to formally approach these questions. Specifically, we develop a test which allows to make rigorous confidence statements about which time trends are different and where (that is, in which time intervals) they differ. Based on our multiscale test, we further develop a clustering algorithm which allows to cluster the observed time series into groups with the same trend. We derive asymptotic theory for our test and clustering methods. The theory is complemented by a simulation study and two applications to GDP growth data and house pricing data.