Consistent Functional Pca for Financial Time-series

Functional Principal Component Analysis (FPCA) provides a powerful and natural way to model functional financial data sets (such as collections of time-indexed futures and interest rate yield curves). However, FPCA assumes each sample curve is drawn from an independent and identical distribution. This assumption is axiomatically inconsistent with financial data; rather, samples are often interlinked by an underlying temporal dynamical process. We present a new modeling approach using Vector auto-regression (VAR) to drive the weights of the principal components. In this novel process, the temporal dynamics are first learned and then the principal components extracted. We dub this method the VAR-FPCA. We apply our method to the NYMEX light sweet crude oil futures curves and demonstrate that it contains significant advantages over the conventional FPCA in applications such as statistical arbitrage and risk management.