Function Space Trend Determination using Machine Learning

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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.