A Time-Varying Autoregressive Model for Characterizing Nonstationary Processes

This letter presents a time-varying autoregressive (TVAR) model aiming to characterize nonstationary behaviors often observed in real-world processes, which cannot be properly described by autoregressive processes such as first-order Markov and random-walk models. Specifically, general model expressions for the mean vector and covariance matrix of the TVAR model are firstly derived. Then, such expressions are used to guide the design of two special setups for the TVAR model. The capability of the developed model to reproduce important nonstationary behaviors is verified mathematically and through simulations.