Rank and Factor Loadings Estimation in Time Series Tensor Factor Model by Pre-averaging
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预平均法估计时间序列张量因子模型的秩与因子载荷
- 研究问题
- 当张量时间序列的特异成分存在序列与横截面相关、变量仅有有界四阶矩时，如何估计各维因子载荷空间和因子秩？
- 方法与思路
- 作者沿张量纤维预平均以汇集信息，再利用最强因子的估计方向投影数据并重新估计载荷空间，同时借助投影后的相关信息估秩。
- 材料陈述的贡献
- 摘要称给出载荷空间估计的理论保证和收敛率，提出新的秩估计方法，并以模拟及矩阵形式投资组合收益数据展示表现。
- 阅读关注点
- 应核对因子强度、维度增长及特异相关的限制，比较初次估计与投影再估计的收敛率，并检查秩选择所需的信号条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；摘要未列出完整依赖条件或收敛率，模拟中的竞争力不等于全面优于其他方法。
原文摘要
Tensor time series data appears naturally in a lot of fields, including finance and economics. As a major dimension reduction tool, similar to its factor model counterpart, the idiosyncratic components of a tensor time series factor model can exhibit serial correlations, especially in financial and economic applications. This rules out a lot of state-of-the-art methods that assume white idiosyncratic components, or even independent/Gaussian data. While the traditional higher order orthogonal iteration (HOOI) is proved to be convergent to a set of factor loading matrices, the closeness of them to the true underlying factor loading matrices are in general not established, or only under some strict circumstances like having i.i.d. Gaussian noises (Zhang and Xia, 2018). Under the presence of serial and cross-correlations in the idiosyncratic components and time series variables with only bounded fourth order moments, we propose a pre-averaging method that accumulates information from tensor fibres for better estimating all the factor loading spaces. The estimated directions corresponding to the strongest factors are then used for projecting the data for a potentially improved re-estimation of the factor loading spaces themselves, with theoretical guarantees and rate of convergence spelt out. We also propose a new rank estimation method which utilizes correlation information from the projected data, in the same spirit as Fan, Guo and Zheng (2022) for factor models with independent data. Extensive simulation results reveal competitive performance of our rank and factor loading estimators relative to other state-of-the-art or traditional alternatives. A set of matrix-valued portfolio return data is also analyzed.