New Methods and Theory for the Comparison of Nonparametric Trend Curves

该项目的主要目的是为非参数时间趋势曲线的分析发展新的方法和理论。近年来，人们对具有非参数和半参数时间趋势的计量经济模型越来越感兴趣。非参数和半参数趋势建模在面板数据环境中引起了特别的兴趣。重要的问题是，面板中观察到的时间序列是否都具有相同的趋势，或者它们是否可以聚在具有相同趋势的组中。文献中已经开发了许多测试和聚类方法来处理这些问题，这些问题与各种经济和金融应用相关。然而，大多数提出的方法依赖于一些带宽或平滑参数，其最佳选择是一个众所周知的难题。在我们的项目中，我们解决了开发新的测试和聚类方法的挑战，这些方法不需要经典的带宽参数，从而避免了带宽选择的问题。为了实现这一点，我们将建立在最近被引入文献的统计多尺度测试技术的基础上。该项目的方法和理论分析将辅以模拟和实证应用。特别是，我们打算将开发的方法应用于宏观经济学中感兴趣的经验问题，即某些国家的实际GDP增长是否比其他国家更快的问题。

The main purpose of the project is to develop new methods and theory for the analysis of nonparametric time trend curves. Recently, there has been a growing interest in econometric models with non- and semiparametric time trends. Non- and semiparametric trend modelling has attracted particular interest in a panel data context. Important questions are whether the observed time series in the panel all have the same trend or whether they can be clustered into groups with the same trend. A number of test and clustering methods have been developed in the literature to approach these questions, which are relevant in a variety of economic and financial applications. Most of the proposed methods, however, depend on a number of bandwidth or smoothing parameters whose optimal choice is a notoriously difficult problem. In our project, we tackle the challenge of developing new test and clustering methods which are free of classic bandwidth parameters and thus avoid the issue of bandwidth selection. To achieve this, we will build on techniques from statistical multiscale testing which have recently been introduced into the literature. The methodological and theoretical analysis of the project will be complemented by simulations and empirical applications. In particular, we intend to apply the developed methods to an empirical question of interest in macroeconomics, that is, the question of whether real GDP growth has been faster in some countries than in others.