Analysis of Multistate Autoregressive Models

In this paper, we consider the inference problem for a wide class of time-series models, referred to as multistate autoregressive models. The time series that we consider are composed of multiple epochs, each modeled by an autoregressive process. The number of epochs is unknown, and the transitions of states follow a Markov process of an unknown order. We propose an inference strategy that enables reliable and efficient offline analysis of this class of time series. The inference is carried out through a three-step approach: detecting the structural changes of the time series using a recently proposed multiwindow algorithm, identifying each segment as a state and selecting the most appropriate number of states, and estimating the Markov source based upon the symbolic sequence obtained from previous steps. We provide theoretical results and algorithms in order to facilitate the inference procedure described above. We demonstrate the accuracy, efficiency, and wide applicability of the proposed algorithms via an array of experiments using synthetic and real-world data.