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.

翻译：金融时间序列通常可分解为市场因子（捕捉资产间共同的价格变动）与残差因子（反映资产特异性偏离）。为对冲全市场风险（如新冠疫情冲击），利用残差因子的交易策略已被证明具有有效性。然而，金融时间序列常呈现近奇异的特征结构，这阻碍了残差因子的稳定准确估计。本文提出一种从金融时间序列中提取残差因子的方法，该方法分层应用主成分分析（PCA）与高斯图模型（GGM）。我们的分层方法在稳定估计与消除仅靠PCA无法完全去除的因子之间取得平衡，从而实现了残差因子的高效提取。我们采用二阶多元全正（MTP2）约束的GGM以捕捉金融数据中普遍存在的正相关性。分析证明，所得残差因子比仅使用PCA获取的因子具有更强的正交性。在测试周期与训练集长度各异的多次实验中，所提方法均能持续实现更优的残差因子正交性。对S&P 500与TOPIX 500成分股的回溯测试进一步表明交易绩效得到改善，包括更高的夏普比率。