Estimation of Sparsity-Induced Weak Factor Models
研究了稀疏诱导弱因子模型的估计方法，允许特征值以不同速率增长，并提出了优于主成分估计的新估计量，应用于债券收益率预测和股票收益分析。
This article investigates estimation of sparsity-induced weak factor (sWF) models, with large cross-sectional and time-series dimensions (<i>N</i> and <i>T</i>, respectively). It assumes that the <i>k</i>th largest eigenvalue of a data covariance matrix grows proportionally to Nαk with unknown exponents 0<αk≤1 for k=1,…,r. Employing the same rotation of the principal components (PC) estimator, the growth rate <i>α<sub>k</sub></i> is linked to the degree of sparsity of <i>k</i>th factor loadings. This is much weaker than the typical assumption on the recent factor models, in which all the <i>r</i> largest eigenvalues diverge proportionally to <i>N</i>. We apply the method of sparse orthogonal factor regression (SOFAR) by Uematsu et al. (2019) to estimate the sWF models and derive the estimation error bound. Importantly, our method also yields consistent estimation of <i>α<sub>k</sub></i>. A finite sample experiment shows that the performance of the new estimator uniformly dominates that of the PC estimator. We apply our method to forecasting bond yields and the results demonstrate that our method outperforms that based on the PC. We also analyze S&P500 firm security returns and find that the first factor is consistently near strong while the others are weak.