论文标题
具有潜在组结构的矩阵值式网络自动收入模型
Matrix-valued Network Autoregression Model with Latent Group Structure
论文作者
论文摘要
矩阵值估计的时间序列数据经常在广泛的区域中观察到，并且最近引起了人们的关注。在这项工作中，我们在矩阵自动收入框架中为高维矩阵值值的时间序列数据建模网络效应。为了表征受试者的潜在异质性并同时处理高维度，我们假设每个受试者都有一个潜在的组标签，这使我们能够将主体聚集到相应的行和列组中。我们提出了一个组矩阵网络自动进度（GMNAR）模型，该模型假设同一组中的受试者共享相同的模型参数。为了估计模型，我们开发了一种迭代算法。从理论上讲，我们表明，当组号正确或可能过度指定时，可以始终估算小组参数和组成员身份。还提供了针对小组编号估计的信息标准，以始终如一地选择组号。最后，我们在Yelp数据集上实现了该方法，以说明该方法的实用性。
Matrix-valued time series data are frequently observed in a broad range of areas and have attracted great attention recently. In this work, we model network effects for high dimensional matrix-valued time series data in a matrix autoregression framework. To characterize the potential heterogeneity of the subjects and handle the high dimensionality simultaneously, we assume that each subject has a latent group label, which enables us to cluster the subject into the corresponding row and column groups. We propose a group matrix network autoregression (GMNAR) model, which assumes that the subjects in the same group share the same set of model parameters. To estimate the model, we develop an iterative algorithm. Theoretically, we show that the group-wise parameters and group memberships can be consistently estimated when the group numbers are correctly or possibly over-specified. An information criterion for group number estimation is also provided to consistently select the group numbers. Lastly, we implement the method on a Yelp dataset to illustrate the usefulness of the method.
