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.
We propose a one-shot mechanism for high-energy cosmic ray generation by a neutron star falling into a black hole surrounded by low density plasma. The function of the black hole in this scenario is to accelerate the star to a speed arbitrarily close
to that of light. When the star - essentially, a magnetized sphere - approaches the horizon it imparts energy to the ambient plasma charges via the induced electric field. Disregarding radiation losses, for iron nucleus, a simple estimate gives energies on the order of 10^19 eV for stars with magnetic fields as weak as 10^6 teslas. The proposed mechanism should also work in chance encounters between rapidly moving neutron stars and molecular clouds. The rarity of such encounters may explain the apparent randomness and rarity of the high-energy cosmic ray events.
