Sequential learning of Multi-state autoregressive time series

Modeling and forecasting streaming data has fundamental importance in many real world applications. In this paper, we present an online model selection technique that can be used to model non-stationary time series in a sequential manner. Multi-state autoregressive (AR) model is used to describe non-stationary time series, and a dynamic algorithm is applied to learn the states at each time step. The proposed technique estimates a candidate AR filter from the most recent data points at every time step, and checks whether starting a new state significantly decreases prediction error or not. To that end, a time-varying threshold is compared with the reduction in the prediction error caused by postulating a new AR filter. The threshold is calculated by sampling and clustering uniformly distributed stable AR filters. Numerical simulations show that the proposed algorithm accurately estimates the state transitions with a small delay.