Center for Industrial Mathematics and Statistics » REU 2021 – Decorrelation Detection in a Financial Time Series Data Set

Nicholas Gawron

Aaron Stapleton

Austin Sibu

Grace Johnson

Overview

Industrial Sponsor: Wellington Management

Industrial Liaisons: Dr. Henri Fouda, Mr. Ravi Shastri

Faculty Advisors: Dr. Fangfang Wang, WPI

Dimension estimation (DE) contains a broad set of tools that can be used to determine whether seemingly diversified index fund portfolios in fact have latent commonalities that increase risk for investors. Principal Component Analysis (PCA) is the widely used statistical tool for dimension estimation. However, during periods of financial crisis, PCA is unable to adequately perform dimension estimation, because it relies on linear relationships and is sensitive to outliers. In this project, we investigate robust and nonlinear techniques including Robust PCA (RPCA) and autoencoders, assessing their usefulness for three tasks: dimension estimation, data reconstruction, and correlation visualization. To optimize performance, we conduct extensive empirical analyses
that investigate the efficacy of the sparsity parameter in RPCA in forcing a
lower dimension approximation of the original data and explore the accuracy of reconstructions from autoencoders being passed through RPCA as a means of improving DE results. We find several methods that are resistant to market shocks, including RPCA and our own kitchen sink approach, which combines RPCA and autoencoders for pre-processing data before applying PCA. We also develop a novel method to estimate dimension using autoencoders. Finally, we discuss the usefulness of each technique with respect to each of the three tasks and provide insight into future time series modeling.