Time series clustering based on prediction accuracy of global forecasting models

Abstract

[Abstract]: We present a novel model-based time series clustering technique. Rather than fitting a model to each time series in isolation and then clustering the estimated model coefficients, our approach finds partitions where a single model accurately represents the entire group. This strategy exploits the inherent similarity between time series to get better model estimates, resulting in more robust and informative clusters. The models fitted to each partition deviate from the classic, ‘local’ time series model classes such as the ARIMA and instead follow the recent so-called ‘global’ forecasting models or cross-learning paradigm. Global models achieve superior predictive accuracy by fitting a more complex model class to the pool of time series in a dataset. This way, similarity information is better exploited and minor sources of heterogeneity are captured by the increased complexity. The procedure has a key additional main benefit. The problem of selecting the number of clusters, often separate from the partitioning process and subjective to the analyst, is completely solved in our case: the number of clusters that optimizes the predictive accuracy of the underlying global forecasting models should be chosen. In an extensive simulation and real-data study, we provide evidence of this approach outperforming reference techniques in both clustering quality and predictive accuracy. As the procedure is agnostic to the choice of the forecasting model, it can be combined with any model class. We provide examples of interpretation for linear models.