Deep Time: Deep Learning Extensions to Time Series Factor Analysis with Applications to Uncertainty Quantification in Economic and Financial Modeling

This thesis establishes methods to quantify and explain uncertainty through high-order moments in time series data, along with first principal-based improvements on the standard autoencoder and variational autoencoder. While the first-principal improvements on the standard variational autoencoder provide additional means of explainability, we ultimately look to non-variational methods for quantifying uncertainty under the autoencoder framework. We utilize Shannon's differential entropy to accomplish the task of uncertainty quantification in a general nonlinear and non-Gaussian setting. Together with previously established connections between autoencoders and principal component analysis, we motivate the focus on differential entropy as a proper abstraction of principal component analysis to this more general framework, where nonlinear and non-Gaussian characteristics in the data are permitted. Furthermore, we are able to establish explicit connections between high-order moments in the data to those in the latent space, which induce a natural latent space decomposition, and by extension, an explanation of the estimated uncertainty. The proposed methods are intended to be utilized in economic and financial factor models in state space form, building on recent developments in the application of neural networks to factor models with applications to financial and economic time series analysis. Finally, we demonstrate the efficacy of the proposed methods on high frequency hourly foreign exchange rates, macroeconomic signals, and synthetically generated autoregressive data sets.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2022

Author dc:creator

• Miller, Dawson Jon

Chair dc:contributor.committeechair

• Embree, Mark P.

Committee members dc:contributor.committeemember

• Habibnia, Ali
• Hewett, Russell Joseph

• Uncertainty Quantification
• High-Order Moments
• Deep Learning
• Neural Networks
• Autoencoders
• Variational Autoencoders
• Metropolis-Hastings
• High Frequency
• Economics
• Finance
• Foreign Exchange Rates
• Distribution Estimation
• Factor Models

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:35501

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/111804