Factor modeling for high-dimensional time series: Inference for the number of factors
高维时间序列因子建模：因子个数的推断AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究高维平稳时间序列的因子建模、载荷与因子个数估计。
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高维时间序列因子建模：因子个数的推断
- 研究问题
- 在平稳高维时间序列中，如何估计因子个数与载荷，并在维度随样本量增长及因子强度不同时保持有效？
- 方法与思路
- 作者对非负定矩阵进行特征分析，以估计特征值之比判断因子个数，并研究不同因子强度下的两步程序。
- 材料陈述的贡献
- 摘要称，即使高维情形下特征值估计不一致，因子个数估计仍可有效；特定条件下，维度增加还可能改善表现。
- 阅读关注点
- 核对平稳性、因子强度和维度增长条件，查看特征值比值准则、两步程序及所谓维度增益成立的范围。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；摘要未列出完整条件，维度增益及因子个数估计有效性均不能无条件推广。
原文摘要
This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are estimated in terms of an eigenanalysis for a nonnegative definite matrix, and is therefore applicable when the dimension of time series is on the order of a few thousands. Asymptotic properties of the proposed method are investigated under two settings: (i) the sample size goes to infinity while the dimension of time series is fixed; and (ii) both the sample size and the dimension of time series go to infinity together. In particular, our estimators for zero-eigenvalues enjoy faster convergence (or slower divergence) rates, hence making the estimation for the number of factors easier. In particular, when the sample size and the dimension of time series go to infinity together, the estimators for the eigenvalues are no longer consistent. However, our estimator for the number of the factors, which is based on the ratios of the estimated eigenvalues, still works fine. Furthermore, this estimation shows the so-called “blessing of dimensionality” property in the sense that the performance of the estimation may improve when the dimension of time series increases. A two-step procedure is investigated when the factors are of different degrees of strength. Numerical illustration with both simulated and real data is also reported.