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.

翻译：高维矩阵型数据在金融和经济学中频繁出现，且常跨越较长时间跨度，例如涵盖多个国家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背景，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其隐含的动态结构，并实现降维。在允许噪声在时间、行或列方向存在弱相关的一般条件下，我们建立了估计量的一致性和渐近正态性。本文引入了一种新方法以克服估计量中的旋转模糊性问题，从而提高估计载荷矩阵的清晰度和可解释性。模拟研究突显了所提估计量的优势以及平滑操作的有效性。在应用于国际贸易流量时，我们探究了贸易网络中的交易枢纽、中心性、模式及趋势。