Switching vector autoregressive models with higher-order regime dynamics Application to prognostics and health management

Regime switching vector autoregressive (RSVAR) models are typically used to model changing dependency structures of multivariate time series. These changing regimes are represented by using a first-order Markov process where the transition distribution reflects the probabilities of moving to one of the other regime in the subsequent time step. Instead of representing the state of the system at different points in time, we extend this framework by using an explicit time representation that allows us to query against probability distributions of when particular regime changes take place. In contrast to continuous time based approaches such as continuous time Bayesian networks or continuous time Markov processes, we do not rely on intensity matrices that describe trajectories of consecutive states. Here we define regime changes as events and understand time as context of an event. This allows us to integrate dependencies at different time granularities while being able to perform inference in a decomposed way. As a consequence, we can efficiently consider higher-order effects stretching across a large number of consecutive regimes. The underlying assumption is that timely evolution of variables between regime switches is completely captured by the VAR model or possibly a set of VAR models with varying measuring rates and that there is a representative set of multiple time series exhibiting similar higher-order regime dynamics. In this paper we show how such dynamics can be learned integrative with learning RSVAR model parameters and how the regime dynamics can be considered in the RSVAR inference procedures. We demonstrate the benefits of our approach based on a simple scenario. Further, an application to a typical prognostics scenario is presented, leading to the highest score in the IEEE PHM 2014 Data Challenge for the industrial track.