Correlation networks, dynamic factor models and community detection

TL;DR

This paper introduces a unified framework combining dynamic factor models, mixture distributions, and community detection to analyze high-dimensional multivariate time series, revealing block correlation structures and clustering components effectively.

Contribution

It presents a novel integration of mixture dynamic factor models with network community detection, providing bounds on clustering accuracy and applying the method to real and simulated data.

Findings

Effective clustering of time series into communities

Block correlation structures identified in high-dimensional data

Method demonstrated on real and simulated datasets

Abstract

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.