因子模型的一种结构突变检验及其统计性质研究

为了内生地识别动态因子模型因子载荷矩阵的结构突变（包括因子个数的变化），本文利用主成分估计得伪因子序列构造累积平方和统计量检验因子载荷矩阵的结构突变性，进一步利用迭代累积平方和算法对多个结构突变点的位置进行探测。研究发现，本文提出的检验统计量对于因子个数误设具有稳健性；并且该检验具有良好的有限样本性质和渐近性；另外，实证分析发现，中国沪市A股市场制造业上市公司的对数收益率序列存在结构突变的共同因子。

A Test of Structural Changes in Dynamic Factor Models and Their Statistical Properties

In order to endogenously ascertain the structural changes of factor loading matrix in dynamic factor models, this paper obtains a cumulative sum of squares statistic for the estimated pseudo factor sequences by using the principal component estimation to test the structural changes of factor loading matrix. Furthermore, the iterative cumulative sum of squares algorithm is applied to detect the positions of the change points. It is found that the testing statistic proposed in this paper is robust as to the biased number of factors set. Moreover, there are good finite sample and asymptotic convergence properties in the statistic. In addition, an empirical analysis shows that there are common factors of structural changes in the logarithmic return sequence of the listed companies in the A-Shares of the Shanghai Stock Exchange.