Autoregressive mixture models for clustering time series

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.

Modelling the complexity of pandemic-related lifestyle quality change and mental health: an analysis of a nationally representative UK general population sample.

PURPOSE: The COVID-19 pandemic has affected the way many individuals go about their daily lives. This study attempted to model the complexity of change in lifestyle quality as a result of the COVID-19 pandemic and its context within the UK adult population. METHODS: Data from the COVID-19 Psychological Research Consortium Study (Wave 3, July 2020; N = 1166) were utilised. A measure of COVID-19-related lifestyle change captured how individuals' lifestyle quality had been altered as a consequence of the pandemic. Exploratory factor analysis and latent profile analysis were used to identify distinct lifestyle quality change subgroups, while multinomial logistic regression analysis was employed to describe class membership. RESULTS: Five lifestyle dimensions, reflecting partner relationships, health, family and friend relations, personal and social activities, and work life, were identified by the EFA, and seven classes characterised by distinct patterns of change across these dimensions emerged from the LPA: (1) better overall (3.3%), (2) worse except partner relations (6.0%), (3) worse overall (2.5%), (4) better relationships (9.5%), (5) better except partner relations (4.3%), (6) no different (67.9%), and (7) worse partner relations only (6.5%). Predictor variables differentiated membership of classes. Notably, classes 3 and 7 were associated with poorer mental health (COVID-19 related PTSD and suicidal ideation). CONCLUSIONS: Four months into the pandemic, most individuals' lifestyle quality remained largely unaffected by the crisis. Concerningly however, a substantial minority (15%) experienced worsened lifestyles compared to before the pandemic. In particular, a pronounced deterioration in partner relations seemed to constitute the more severe pandemic-related lifestyle change.