Generalized Principal Component Analysis

The primary objective of this dissertation is to extend the classical Principal Components Analysis (PCA), aiming to reduce the dimensionality of a large number of Normal interrelated variables, in two directions. The first is to go beyond the static (contemporaneous or synchronous) covariance matrix among these interrelated variables to include certain forms of temporal (over time) dependence. The second direction takes the form of extending the PCA model beyond the Normal multivariate distribution to the Elliptically Symmetric family of distributions, which includes the Normal, the Student's t, the Laplace and the Pearson type II distributions as special cases. The result of these extensions is called the Generalized principal component analysis (GPCA). The GPCA is illustrated using both Monte Carlo simulations as well as an empirical study, in an attempt to demonstrate the enhanced reliability of these more general factor models in the context of out-of-sample forecasting. The empirical study examines the predictive capacity of the GPCA method in the context of Exchange Rate Forecasting, showing how the GPCA method dominates forecasts based on existing standard methods, including the random walk models, with or without including macroeconomic fundamentals.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Economics

Department dc:contributor.department

Economics, Science

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2018

Author dc:creator

• Solat, Karo

Chair dc:contributor.committeechair

• Spanos, Aris

Committee members dc:contributor.committeemember

• Bahel, Eric A.
• Ashley, Richard A.
• Tsang, Kwok Ping
• Maasoumi, Esfandiar

• Factor Model
• PCA
• Elliptically Contoured Distributions
• Exchange Rate
• Forecasting
• Monte Carlo Simulation
• Statistical Adequacy

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

vt_gsexam:15413

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/83469