Denoising and Multilinear Projected-Estimation of High-Dimensional Matrix-Variate Factor Time Series
高维矩阵因子时间序列的去噪与多线性投影估计AI 解读 ↓
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高维矩阵因子时间序列的去噪与多线性投影估计
- 研究问题
- 当高维矩阵时间序列包含低维动态因子，且特异项具有尖峰或发散协方差特征值时，如何降低噪声并估计因子结构。
- 方法与思路
- 作者采用迭代多线性投影估计载荷，以双向投影主成分分析抑制发散噪声，并用高维白噪声检验估计矩阵因子维数。
- 材料陈述的贡献
- 摘要称，该方法具有高维渐近性质及更快收敛速度，模拟和真实例子的样本外预测表现良好，补充材料还考察特异项序列相关。
- 阅读关注点
- 应核对因子与特异项结构的区分、维数和样本量的增长条件，以及收敛率比较、维数检验和预测评测采用的基准。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未给出收敛率公式和预测数值，补充扩展的条件也未展开。
原文摘要
This paper proposes a new multi-linear projection method for denoising and estimation of high-dimensional matrix-variate factor time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent, lower-dimensional matrix-variate factor process and a $p_1\times p_2$ matrix idiosyncratic series. In addition, the latter series assumes a matrix-variate factor structure such that its row and column covariances may have diverging/spiked eigenvalues to accommodate the case of low signal-to-noise ratio often encountered in applications. We use an iterative projection procedure to reduce the dimensions and noise effects in estimating front and back loading matrices and to obtain faster convergence rates than those of the traditional methods available in the literature. We further introduce a two-way projected Principal Component Analysis to mitigate the diverging noise effects, and implement a high-dimensional white-noise testing procedure to estimate the dimension of the matrix factor process. Asymptotic properties of the proposed method are established if the dimensions and sample size go to infinity. We also use simulations and real examples to assess the performance of the proposed method in finite samples and to compare its forecasting ability with some existing ones in the literature. The proposed method fares well in out-of-sample forecasting. In a supplement, we demonstrate the efficacy of the proposed approach even when the idiosyncratic terms exhibit serial correlations with or without a diverging white noise effect.