Iterated and exponentially weighted moving principal component analysis

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 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.