  We present an approach to clustering time series data using a model-based
generalization of the K-Means algorithm which we call K-Models. We prove the
convergence of this general algorithm and relate it to the hard-EM algorithm
for mixture modeling. We then apply our method first with an AR($p$) clustering
example and show how the clustering algorithm can be made robust to outliers
using a least-absolute deviations criteria. We then build our clustering
algorithm up for ARMA($p,q$) models and extend this to ARIMA($p,d,q$) models.
We develop a goodness of fit statistic for the models fitted to clusters based
on the Ljung-Box statistic. We perform experiments with simulated data to show
how the algorithm can be used for outlier detection, detecting distributional
drift, and discuss the impact of initialization method on empty clusters. We
also perform experiments on real data which show that our method is competitive
with other existing methods for similar time series clustering tasks.
