Prediction error methods in learning jump ARMAX models

Jump models describe systems that change their dynamics over time. Identifying jump models amounts both to learn the behavior of the system at each operating mode and to reconstruct the active mode sequence from data. This paper focuses on the identification of jump autoregressive moving-average models with exogenous inputs (JARMAX), combining prediction error methods with a coordinate descent algorithm for fitting jump models. The resulting identification algorithm alternates between minimizing the sum of prediction errors with respect to the parameters of the ARMAX models, and minimizing a discrete loss function with respect to the sequence of active modes.