Function Space Trend Determination using Machine Learning

在社会经济话语中，关于经济增长、不平等、福利和跨地区、跨国家的经济差距的趋势随处可见。它们在许多经济理论和其他科学研究领域发挥着重要作用。趋势确定方法在经济学中已经被深入研究了很长一段时间，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。这项研究计划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。目标是在对趋势行为的性质几乎没有实际或理论指导的情况下对趋势进行建模。将制定各种方法，以了解一般功能空间环境中的趋势，使其能够广泛应用于研究社会经济现象。这些方法将在其他科学领域有用，例如气候变化，这些领域的趋势很重要。该项目将开发和分析一种易于实施的机器学习程序，以增强现有数据平滑和过滤方法的特性。其核心思想是以受控的方式迭代这样的过滤器，使它们成为确定趋势的更智能的平滑工具。这种方法涉及基于Booking的机器学习方法，该项目将开发必要的理论，以证明它们适用于表现出趋势行为的非平稳数据。特别是，该项目将开发增强型过滤器的大样本极限理论，揭示其增强的能力，重点是在非平稳数据的背景下分析增强型方法的性质这一复杂任务，非平稳数据的特征是确定性和随机性趋势，也允许可能的结构突变。由此产生的理论将适用于广泛的潜在过程类别，从而促进在经济学和其他需要确定趋势的学科的实际工作中知情地使用这种机器学习设备。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.