论文标题
具有统计保证的大维时间序列的分位数因子分析
Quantile factor analysis for large-dimensional time series with statistical guarantee
论文作者
论文摘要
分位数是服务行业金融和质量评估的重要措施。在本文中，我们通过潜在分位数模型对大维时间序列的分位数的时间和横截面交互作用进行了建模。通过迭代检查损失最小化程序，通过统计保证学习了因子负载和分数。在任何时刻限制的情况下，我们可以正确地确定每个变量的常见和特质组件。我们获得了最小化估计量的统计收敛速率。在某些轻度条件下提供了估计因子负荷和得分的巴哈德尔表示。此外，提出了一种坚固的方法来始终选择因素数量。模拟实验检查了理论的有效性。我们对财务数据集的分析表明，在投资组合分配中学习分位数的优越性比学习平均因素的其他最先进的方法的优势。
Quantile is an important measure in finance and quality assessment in service industry. In this paper, we model the temporal and cross-sectional interactive effect of the quantiles of large-dimensional time series by a latent quantile factor model. The factor loadings and scores are learnt with statistical guarantee via an iterative check-loss-minimization procedure. Without any moment constraint on the idiosyncratic errors, we correctly identify the common and idiosyncratic components for each variable. We obtained the statistical convergence rates of the minimization estimators. Bahardur representations for the estimated factor loadings and scores are provided under some mild conditions. Moreover, a robust method is proposed to select the number of factors consistently. Simulation experiments checked the validity of the theory. Our analysis on a financial data set shows the superiority of learning quantile factors in portfolio allocation over other state-of-the-art methods that learn mean factors.
