Function Space Trend Determination using Machine Learning

在关于经济增长、不平等、福利以及跨地区和国家的经济差距的社会经济话语中，趋势无处不在。它们在许多经济理论和其他科学研究领域中发挥着重要作用。长期以来，经济学对趋势确定的方法进行了深入研究，但经济学家对趋势行为的来源和性质几乎没有指导，因此在应用中依赖于有限类别的模型。这个研究项目将探索一种新的方法来研究涉及现代机器学习方法的趋势。目标是在几乎没有关于趋势行为本质的实际或理论指导的情况下对趋势进行建模。将发展各种方法来了解一般功能空间环境中的趋势，以便广泛应用于研究社会经济现象。这些方法在其他科学领域也很有用，比如气候变化，在这些领域，趋势是很重要的。该项目将开发和分析一个易于实现的机器学习程序，以增强现有平滑和过滤数据方法的特性。中心思想是以一种可控的方式迭代这种过滤器，使其成为趋势确定的更智能的平滑设备。这种方法涉及基于提升的机器学习方法，该项目将开发必要的理论来证明它们在表现趋势行为的非平稳数据中的应用。特别是，该项目将为增强滤波器开发一个大样本极限理论，这将揭示其增强的能力，重点关注在以确定性和随机趋势为特征的非平稳数据背景下分析增强方法特性的复杂任务，也允许可能的结构断裂。由此产生的理论将适用于广泛的底层过程，从而促进在经济学和其他需要趋势确定的学科的实际工作中明智地使用这种机器学习设备。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Trends are found everywhere in socio-economic discourse about economic growth, inequality, welfare, and economic disparities across regions and nations. They play an important role in much economic theory and other areas of scientific research. Methods of trend determination have been intensively studied in economics for a long time, yet economists have little guidance on the source and nature of trend behavior and therefore rely on a limited class of models to use in applications. This research program will explore a new approach to studying trends that involves modern machine learning methods. The goal is to model trends when there is little practical or theoretical guidance about the nature of the trending behavior. Methods will be developed to learn about trends in a general function space environment that will enable wide application to study socio-economic phenomena. These methods will be useful in other scientific fields, such as climate change, where trends figure prominently. The project will develop and analyze an easy-to-implement machine learning procedure that enhances the properties of existing methods of smoothing and filtering data. The central idea is to iterate such filters in a controlled manner to make them a smarter smoothing device for trend determination. This approach involves methods of machine learning based on boosting and the project will develop the necessary theory to justify their application to non-stationary data that manifest trend behavior. In particular, the project will develop a large sample limit theory for boosted filters that will reveal its enhanced capabilities, focusing on the complex task of analyzing properties of the boosting methodology in the context of non-stationary data characterized by deterministic and stochastic trends allowing also for possible structural breaks. The resulting theory will be applicable to a wide class of underlying processes, thereby facilitating informed use of such machine learning devices in practical work in economics and other disciplines where trend determination is needed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.