基于矩阵值因子模型的高维已实现协方差矩阵建模
发布时间：2019-08-03 17:16
【摘要】：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。
[Abstract]:With the advent of big data's era, the dimension of data to be analyzed is getting higher and higher. The estimation and modeling of high-dimensional covariance matrix has become a basic problem in the field of statistics. In this paper, a predictable matrix value factor model based on Cholesky decomposition is proposed, and the high dimensional realized covariance matrix is modeled and predicted. The model effectively reduces the matrix dimension, significantly reduces the number of parameters to be estimated, and effectively avoids the accumulation of estimation errors, and the factor analysis reduces the dimension to make the dependent relationship between the elements of the covariance matrix clearer. The actual modeling results show that the prediction error of the model is close to that of the VAR-LASSO method, but the dimensionality reduction effect is more obvious, the number of parameters to be estimated is greatly reduced, and it has more application value. The portfolio return based on matrix value factor model is closer to the real portfolio return and more robust than the VAR-LASSO method.
【作者单位】： 中央财经大学统计与数学学院;中国现场统计研究会;中国现场统计研究会统计综合评价研究分会;
【基金】：国家自然科学基金面上项目“稳健投资组合选择的并行最优化算法研究与实现”(61272193) 中央财经大学研究生科研创新基金项目“高维协方差阵建模及投资组合应用”(201607)资助
【分类号】：O212.1
[Abstract]:With the advent of big data's era, the dimension of data to be analyzed is getting higher and higher. The estimation and modeling of high-dimensional covariance matrix has become a basic problem in the field of statistics. In this paper, a predictable matrix value factor model based on Cholesky decomposition is proposed, and the high dimensional realized covariance matrix is modeled and predicted. The model effectively reduces the matrix dimension, significantly reduces the number of parameters to be estimated, and effectively avoids the accumulation of estimation errors, and the factor analysis reduces the dimension to make the dependent relationship between the elements of the covariance matrix clearer. The actual modeling results show that the prediction error of the model is close to that of the VAR-LASSO method, but the dimensionality reduction effect is more obvious, the number of parameters to be estimated is greatly reduced, and it has more application value. The portfolio return based on matrix value factor model is closer to the real portfolio return and more robust than the VAR-LASSO method.
【作者单位】： 中央财经大学统计与数学学院;中国现场统计研究会;中国现场统计研究会统计综合评价研究分会;
【基金】：国家自然科学基金面上项目“稳健投资组合选择的并行最优化算法研究与实现”(61272193) 中央财经大学研究生科研创新基金项目“高维协方差阵建模及投资组合应用”(201607)资助
【分类号】：O212.1
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