Maximum-a-posteriori estimation of jump Box-Jenkins models

Complex dynamical systems and time series can often be described by jump models, namely finite collections of local models where each sub-model is associated to a different operating condition of the system or segment of the time series. Learning jump models from data thus requires both the identification of the local models and the reconstruction of the sequence of active modes. This paper focuses on maximum-a-posteriori identification of jump Box-Jenkins models, under the assumption that the transitions between different modes are driven by a stochastic Markov chain. The problem is addressed by embedding prediction error methods (tailored to Box-Jenkins models with switching coefficients) within a coordinate ascent algorithm, that iteratively alternates between the identification of the local Box-Jenkins models and the reconstruction of the mode sequence.