论文标题
测试和支持恢复矩阵值观测的相关结构，并应用于股票市场数据
Testing and Support Recovery of Correlation Structures for Matrix-Valued Observations with an Application to Stock Market Data
论文作者
论文摘要
资产回报的协方差矩阵的估计对于投资组合构建至关重要。正如经济理论所暗示的那样，新兴市场和发达国家之间资产之间的相关结构不同。因此，必须对两组国家之间的相关矩阵平等进行严格的统计推断。但是，如果采用了传统的矢量值方法，则由于与相对丰富的资产相比的国家数量有限，因此由于违反了时间独立性假设而导致的推理是不可行的。这突出了将观测值视为基质值而不是矢量值的必要性。通过矩阵值观测，我们感兴趣的问题可以作为对高斯分布下的协方差结构的统计推断，即测试非相关和相关平等，以及相应的支持估计。我们开发在某些规律条件下渐近最佳的程序。仿真结果证明了我们程序的计算和统计优势，而对于正常分布和非正常分布的某些现有最新方法。我们的程序在股票市场数据中的应用揭示了有趣的模式，并通过严格的统计测试来验证几个经济主张。
Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore imperative to make rigorous statistical inference on correlation matrix equality between the two groups of countries. However, if the traditional vector-valued approach is undertaken, such inference is either infeasible due to limited number of countries comparing to the relatively abundant assets, or invalid due to the violations of temporal independence assumption. This highlights the necessity of treating the observations as matrix-valued rather than vector-valued. With matrix-valued observations, our problem of interest can be formulated as statistical inference on covariance structures under sub-Gaussian distributions, i.e., testing non-correlation and correlation equality, as well as the corresponding support estimations. We develop procedures that are asymptotically optimal under some regularity conditions. Simulation results demonstrate the computational and statistical advantages of our procedures over certain existing state-of-the-art methods for both normal and non-normal distributions. Application of our procedures to stock market data reveals interesting patterns and validates several economic propositions via rigorous statistical testing.
