MODELING TIME SERIES AND SEQUENCES USING MARKOV CHAIN EMBEDDED FINITE AUTOMATA

This paper introduces a new pattern analysis framework, which enables exact and efficient calculation of probabilities of pattern occurrences in time series and general sequences. Statistics of pattern occurrences in data are formulated in terms of finite automata states, and the state transitions are embedded into a Markov chain. This enables pattern analysis of continuous or discrete sequences generated from hidden Markov models, where occurrences of specific patterns in the Markov state sequence is of interest. Through this new methodology, both the joint and marginal distributions of occurrence probabilities of multiple patterns can be obtained in a conceptually simple and computationally efficient way. A novel sequence segmentation methodology utilizing regular languages as pattern definitions is formulated and application of the proposed framework to real data is demonstrated.