Uncovering Residual Factors in Financial Time Series via PCA and MTP2-constrained Gaussian Graphical Models

Abstract: Financial time series are commonly decomposed into market factors, which capture shared price movements across assets, and residual factors, which reflect asset-specific deviations. To hedge the market-wide risks, such as the COVID-19 shock, trading strategies that exploit residual factors have been shown to be effective. However, financial time series often exhibit near-singular eigenstructures, which hinder the stable and accurate estimation of residual factors. This paper proposes a method for extracting residual factors from financial time series that hierarchically applies principal component analysis (PCA) and Gaussian graphical model (GGM). Our hierarchical approach balances stable estimation with elimination of factors that PCA alone cannot fully remove, enabling efficient extraction of residual factors. We use multivariate totally positive of order 2 (MTP2)-constrained GGM to capture the predominance of positive correlations in financial data. Our analysis proves that the resulting residual factors exhibit stronger orthogonality than those obtained with PCA alone. Across multiple experiments with varying test periods and training set lengths, the proposed method consistently achieved superior orthogonality of the residual factors. Backtests on the S&P 500 and TOPIX 500 constituents further indicate improved trading performance, including higher Sharpe ratios.