论文标题
预计的大维矩阵因子模型的估计
Projected Estimation for Large-dimensional Matrix Factor Models
论文作者
论文摘要
在这项研究中，我们提出了一种具有横截面尖刺特征值的大维矩阵因子模型的投影估计方法。通过将观察矩阵投影到行或列因子空间上，我们将矩阵系列的因子分析简化为较低维张量的因子分析。该方法还减少了特质误差组件的幅度，从而增加了信噪比，因为投影矩阵线性过滤了特质误差矩阵。从理论上讲，我们证明了因子加载矩阵的投影估计值比在类似条件下现有估计量更快。还提出了投影估计器的渐近分布。给出了一个新颖的迭代过程，以指定一对行和列因子编号。广泛的数值研究验证了投影方法的经验性能。金融和宏观经济学中的两个真实例子揭示了各行和列之间的因素模式，这与财务，经济或地理解释相吻合。
In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that for a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the pair of row and column factor numbers. Extensive numerical studies verify the empirical performance of the projection method. Two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincides with financial, economic, or geographical interpretations.
