关键词: 矩阵值因子模型, 高维已实现协方差矩阵, Cholesky分解, 向量自回归

Abstract: With the advent of the Big Data Era, the dimension of data is higher and higher, and the problem of modeling high-dimensional covariance 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 displayed 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.

Key words: Matrix-Valued Factor Model, High-dimensional Realized Covariance Matrix, Cholesky Decomposition, VAR