A dynamic factor model with a mixture distribution of the loadings is introduced and studied for multivariate, possibly high-dimensional time series. The correlation matrix of the model exhibits a block structure, reminiscent of correlation patterns for many real multivariate time series. A standard $k$-means algorithm on the loadings estimated through principal components is used to cluster component time series into communities with accompanying bounds on the misclustering rate. This is one standard method of community detection applied to correlation matrices viewed as weighted networks. This work puts a mixture model, a dynamic factor model and network community detection in one interconnected framework. Performance of the proposed methodology is illustrated on simulated and real data.

翻译：本文提出并研究了一种载荷服从混合分布的动态因子模型，适用于多变量（可能为高维）时间序列分析。该模型的相关系数矩阵呈现块状结构，这与许多真实多变量时间序列的相关性模式相吻合。通过主成分估计得到的载荷矩阵，采用标准$k$-均值算法将各分量时间序列聚类为社区，同时给出了误聚类率的上界。这是将相关系数矩阵视为加权网络后进行社区检测的经典方法之一。本研究将混合模型、动态因子模型与网络社区检测整合于一个统一的框架内。通过模拟数据与实际数据验证了所提方法的有效性。