Identifying the number of factors from singular values of a large sample auto-covariance matrix
利用大型样本自协方差矩阵的奇异值识别因子数量AI 解读 ↓
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利用大型样本自协方差矩阵的奇异值识别因子数量
- 研究问题
- 高维因子模型中，哪些因子能从滞后样本自协方差矩阵的奇异值中被检测，以及如何一致估计其数量？
- 方法与思路
- 作者在维度与样本量同比增长的框架下研究因子及噪声的样本奇异值，刻画检测相变并构造因子数估计量。
- 材料陈述的贡献
- 摘要称给出检测相变边界及可检测因子数的强一致估计，因子强度只需超过常数量级边界而无需随维度发散。
- 阅读关注点
- 应核对因子和噪声条件、相变边界的定义，以及显著因子的计数规则、模拟比较与股票收益应用设计。
- 阅读边界
- 材料为稿件版本未注明的 OpenAlex 索引摘要；未给出边界公式和证明条件，优于既有估计的陈述限于所测试情形。
原文摘要
Identifying the number of factors in a high-dimensional factor model has attracted much attention in recent years and a general solution to the problem is still lacking. A promising ratio estimator based on singular values of lagged sample auto-covariance matrices has been recently proposed in the literature with a reasonably good performance under some specific assumption on the strength of the factors. Inspired by this ratio estimator and as a first main contribution, this paper proposes a complete theory of such sample singular values for both the factor part and the noise part under the large-dimensional scheme where the dimension and the sample size proportionally grow to infinity. In particular, we provide an exact description of the phase transition phenomenon that determines whether a factor is strong enough to be detected with the observed sample singular values. Based on these findings and as a second main contribution of the paper, we propose a new estimator of the number of factors which is strongly consistent for the detection of all significant factors (which are the only theoretically detectable ones). In particular, factors are assumed to have the minimum strength above the phase transition boundary which is of the order of a constant; they are thus not required to grow to infinity together with the dimension (as assumed in most of the existing papers on high-dimensional factor models). Empirical Monte-Carlo study as well as the analysis of stock returns data attest a very good performance of the proposed estimator. In all the tested cases, the new estimator largely outperforms the existing estimator using the same ratios of singular values.