Autoregressive mixture models for clustering time series

Abstract

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.

K-ARMA Models for Clustering Time Series Data

“…Several mixture modeling approaches have been developed for time series clustering and classification tasks for which, to our knowledge, hard-clustering analogues have not been developed. Some examples include the work of Xiong and Yeung who develop an EM algorithm for clustering ARMA models [11]; the work of Ren and Barnett who develop an EM algorithm for a Wishart mixture model for clustering time series based on their autocovariance matrices [24]; and the work of Coke and Tsao who develop an EM algorithm for a random effects model for clustering electricity consumers based on their consumption [25]. Theorem 2 says that each of these mixture models has a hard-clustering K-Models analogue.…”