[3D5-GS-2] Machine learning: Time series

[3D5-GS-2-05] Residual return extraction using Principal Component Equivalence method

〇Kentaro Imajo¹, Kei Nakagawa², Kazuki Matoya¹, Masanori Hirano¹, Masana Aoki², Taku Imahase² (1. Preferred Networks, Inc., 2. Nomura Asset Management Co., Ltd.)

Keywords:Financial timeseries, Principal component analysis, Residual returns

In this paper, we focus on the residual returns that are not explained by the common factors in financial asset returns. We propose a novel method to extract well-behaved residual returns based on principal component analysis (PCA). Traditional PCA requires determining the number of common factors, presenting a trade-off: increasing the number reduces common factors but also increases the potential for noise. Our proposed method randomly divides returns into two groups, extracts factors (PC) from one, and estimates eigenvalues from the other. Then, by creating a projection matrix that aims to transform eigenvalues to the same level, the proposed method can extract residual returns with better and more stable properties than PCA. Finally, we demonstrate that our method is capable of extracting residual returns with desirable properties through analysis based on both synthetic and real market data.