Consistent Functional PCA for Financial Time-Series

S. Jaimungal and E.K.H. Ng (Canada)

Keywords

Vector autoregression, functional principal component analysis, risk management, statistical arbitrage, forward curve modeling

Abstract

Functional Principal Component Analysis (FPCA) pro vides a powerful and natural way to model functional fi nancial data sets (such as collections of time-indexed fu tures and interest rate yield curves). However, FPCA as sumes each sample curve is drawn from an independent and identical distribution. This assumption is axiomati cally inconsistent with financial data; rather, samples are often interlinked by an underlying temporal dynamical pro cess. We present a new modeling approach using Vector auto-regression (VAR) to drive the weights of the princi pal components. In this novel process, the temporal dy namics 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 advan tages over the conventional FPCA in applications such as statistical arbitrage and risk management.

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