基于矩阵值因子模型的高维已实现协方差矩阵建模

Modeling High-Dimensional Realized Covariance Matrix Via Matrix-Valued Factor Model

随着大数据时代的来临,待分析数据维度越来越高,高维协方差矩阵的估计与建模已经成为统计学领域的一个基本问题。本文提出基于Cholesky分解的可预测矩阵值因子模型,对高维已实现协方差矩阵进行了建模及预测。模型有效地降低了矩阵维度,显著减少了待估参数数目,有效地避免了估计误差的累积,且因子分析降维使得协方差矩阵元素之间的相依关系更加清晰。实际建模结果表明,模型与VAR-LASSO方法预测误差较为接近,但是降维效果更加明显,待估参数数目大大减少,更加具备应用价值。基于矩阵值因子模型构建的投资组合收益更加贴近真实投资组合收益,而且比VAR-LASSO方法更加稳健。

With the advent of the Big Data Era, the dimension of data is higher and higher, and the problem of modeling high-dimensional covarianee matrix becomes a fundamental issue. In this paper, we propose a novel method called the predictable matrix-valued factor model with the Cholesky decomposition, which could reduce the dimension of matrix effectively and reduce the number of estimated parameters significantly and avoid the aggregated errors. Meanwhile, due to the advantage of factor analysis, the relationships of entries in covariance matrix would be clarified. The consequence of modeling shows that the accuracy of proposed model is disFlayed in accordance with VAR-LASSO method. However, the number of estimated parameters decreases obviously. Lastly, we proceed empirical analysis and we learn that based on the forecasted realized covariance matrix constructed by different method, the final series of return derived from proposed model is more closed to real series of return. Additionally, the proposed model is more robust than VAR-LASSO method.