Iterated and exponentially weighted moving principal component analysis

TL;DR

This paper introduces two new PCA variants, IPCA and EWMPCA, designed to address numerical instability and nonstationarity in financial data using Ogita-Aishima iteration.

Contribution

The paper proposes IPCA and EWMPCA, novel PCA variants that improve stability and adapt to nonstationary data in finance, utilizing Ogita-Aishima iteration.

Findings

IPCA and EWMPCA enhance PCA stability in financial applications.

Both methods effectively handle nonstationary data.

The variants outperform traditional PCA in relevant scenarios.

Abstract

The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical instability and nonstationarity. We attempt to resolve them by proposing two new variants of PCA: an iterated principal component analysis (IPCA) and an exponentially weighted moving principal component analysis (EWMPCA). Both variants rely on the Ogita-Aishima iteration as a crucial step.