时变矩阵因子模型
Time-Varying Matrix Factor Models
AI总结：
本文提出时变矩阵因子模型，利用非参数主成分分析刻画因子载荷的动态变化，并引入新方法解决旋转不确定性，应用于国际贸易网络分析。
摘要：
高维矩阵值数据在金融和经济学中经常被观测到，且跨越较长的时间段，例如众多国家之间国际贸易流量的长期数据。为应对潜在的结构性变化并挖掘矩阵结构的信息内涵，我们提出了一种时变矩阵因子模型。该模型允许因子载荷随时间变化，通过非参数主成分分析揭示潜在的动态结构，并有助于降维。我们在允许噪声在时间、行或列上存在弱相关的一般条件下，建立了估计量的一致性和渐近正态性。我们引入了一种新方法来克服估计量中的旋转不确定性，从而增强所估计载荷矩阵的清晰度和可解释性。我们的模拟研究突显了所提估计量的优点以及平滑操作的有效性。在国际贸易流的应用中，我们研究了贸易网络中的贸易枢纽、中心性、模式和趋势。
英文摘要：
Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural shifts and explore the matrix structure's informational context, we propose a time-varying matrix factor model. This model accommodates changing factor loadings over time, revealing the underlying dynamic structure through nonparametric principal component analysis and facilitating dimension reduction. We establish the consistency and asymptotic normality of our estimators under general conditions that allow for weak correlations across time, rows, or columns of the noise. A novel approach is introduced to overcome rotational ambiguity in the estimators, enhancing the clarity and interpretability of the estimated loading matrices. Our simulation study highlights the merits of the proposed estimators and the effective of the smoothing operation. In an application to international trade flow, we investigate the trading hubs, centrality, patterns, and trends in the trading network.
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