Autoregressive mixture models for clustering time series
提出一种同时聚类和拟合自回归模型的方法，通过Wishart混合模型处理自协方差矩阵，适用于大数据集，并在COVID-19预测中验证效果。
Clustering time series into similar groups can improve models by combining information across like time series. While there is a well developed body of literature for clustering of time series, these approaches tend to generate clusters independently of model training, which can lead to poor model fit. We propose a novel distributed approach that simultaneously clusters and fits autoregression models for groups of similar individuals. We apply a Wishart mixture model so as to cluster individuals while modelling the corresponding autocovariance matrices at the same time. The fitted Wishart scale matrices map to cluster‐level autoregressive coefficients through the Yule–Walker equations, fitting robust parsimonious autoregressive mixture models. This approach is able to discern differences in underlying autocorrelation variation of time series in settings with large heterogeneous datasets. We prove consistency of our cluster membership estimator, asymptotic distributions of coefficients and compare our approach against competing methods through simulation as well as by fitting a COVID‐19 forecast model.