Autoregressive Mixture Models for Serial Correlation Clustering of Time Series Data

Ren, Benny; Barnett, Ian

Clustering individuals into similar groups in longitudinal studies can improve time series models by combining information across like individuals. While there is a well developed literature for clustering of time series, these approaches tend to generate clusters independently of the model training procedure which can lead to poor model fit. We propose a novel method that simultaneously clusters and fits autoregression models for groups of similar individuals. We apply a Wishart mixture model so as to cluster individuals while modeling the corresponding autocorrelation 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 serial variation of time series while accounting for an individual's intrinsic variability. We prove consistency of our cluster membership estimator and compare our approach against competing methods through simulation as well as by modeling regional COVID-19 infection rates.