Beyond PCA for modeling financial time-series

Statistical factor models based on principal component analysis (PCA) have been widely used to reduce the dimensionality of financial time-series. We investigate the sensitivity of PCA to peculiarities of financial data, such as heavy tails and asymmetry and suggest to use alternatives to PCA. We investigate a recent reformulation of principal components as a search for projections which allows to go beyond the squared-error in the objective. We suggest to use a robust formulation for PCA and also a version of PCA with conditional value at risk (cVaR) as the error metric to drive the low-rank approximation. cVaR has received considerable attention in risk management as a coherent replacement of Value at Risk. We describe a convex formulation for both robust PCA and cVaR-PCA and apply them on an computational example with US equities.