Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this question and proposes a new methodology to estimate the correlation matrix which doesn’t depend on the chosen sample period. This new methodology is based on tensor factorization techniques. In particular, combining and normalizing factor components, we build a correlation matrix which shows emerging structural dependency properties not affected by the sample period. To retrieve the factor components, we propose a new tensor decomposition (which we name Slice-Diagonal Tensor (SDT) factorization) and compare it to the two most used tensor decompositions, the Tucker and the PARAFAC. We have that the new factorization is more parsimonious than the Tucker decomposition and more flexible than the PARAFAC. We apply our methodology to simulated datasets using different simulation parameters. Results are robust to different simulation settings and confirm the stability of the correlation matrix generated for two independent samples. The proposed tool applied to two independent samples of empirical data shows that the correlation matrices generated have a block structure representing stock industries. Furthermore, in accordance to two non-parametric tests, namely Kruskal-Wallis and Kolmogorov-Smirnov tests, the correlation matrices are statistically time invariant and hence, stable. Since the resulting correlation matrix is characterized by stability and emerging structural dependency properties, it can be used as alternative to other correlation matrices type of measures, including the Person correlation.

投资组合分配和风险管理利用了相关矩阵，并且严重依赖于要使用的适当相关矩阵的选择。在这方面，一个重要的问题与用于估计稳定的相关矩阵的适当采样周期的选择有关。本文解决了这个问题，并提出了一种新的方法来估计不依赖于所选采样周期的相关矩阵。此新方法基于张量分解技术。特别是，通过组合和归一化因子成分，我们建立了一个相关矩阵，该矩阵显示了不受采样周期影响的新兴结构相关性。要检索因子成分，我们提出了一个新的张量分解（我们将其称为切片对角张量（SDT）分解），并将其与两个最常用的张量分解（塔克和PARAFAC）进行比较。我们认为，新的因式分解比Tucker分解更简洁，并且比PARAFAC更灵活。我们将我们的方法应用于使用不同模拟参数的模拟数据集。结果对不同的仿真设置具有鲁棒性，并确认了为两个独立样本生成的相关矩阵的稳定性。拟议的工具应用于两个独立的经验数据样本表明，生成的相关矩阵具有代表股票行业的块结构。此外，根据两个非参数检验，即Kruskal-Wallis和Kolmogorov-Smirnov检验，相关矩阵在统计上是时不变的，因此是稳定的。由于所得的相关矩阵具有稳定性和新出现的结构相关性的特征，因此可以用作其他相关矩阵类型的度量的替代方法，包括“人”相关性。