## Model-Based Clustering With Hidden Markov Models and its Application to Financial Time-Series Data

**B. Knab, A. Schliep, B. Steckemetz and B. Wichern**

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In **Between Data Science and Applied Data Analysis*, *Springer*, 561–569, 2003. *Proceedings of the GfKl 2002*.

We have developed a method to partition a set of data into clusters by use of Hidden Markov Models. Given a number of clusters, each of which is represented by one Hidden Markov Model, an iterative procedure finds the combination of cluster models and an assignment of data points to cluster models which maximizes the joint likelihood of the clustering. To reflect the partially non-Markovian nature of the data we also extend classical Hidden Markov Models to use a non-homogeneous Markov chain, where the non-homogeneity is dependent not on the time of the observation but rather on a quantity derived from previous observations. We present the method and an evaluation on simulated time-series and large data sets of financial time-series from the Public Saving and Loan Banks in Germany.