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We present an approach to clustering time series data using a model-basedgeneralization of the K-Means algorithm which we call K-Models. We prove theconvergence of this general algorithm and relate it to the hard-EM algorithmfor mixture modeling. We then apply our method first with an AR($p$) clusteringexample and show how the clustering algorithm can be made robust to outliersusing a least-absolute deviations criteria. We then build our clusteringalgorithm 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 basedon the Ljung-Box statistic. We perform experiments with simulated data to showhow the algorithm can be used for outlier detection, detecting distributionaldrift, and discuss the impact of initialization method on empty clusters. Wealso perform experiments on real data which show that our method is competitivewith other existing methods for similar time series clustering tasks.

K-ARMA Models for Clustering Time Series Data