Abstract: This paper proposes a multivariate hysteretic autoregressive model with multiple threshold variables for modeling nonlinear time series. The proposed model encompasses the two-regime multivariate threshold autoregressive model and the hysteretic autoregressive model as special cases. A special feature of the proposed model is that it employs multiple threshold variables, each with a single threshold value. The resulting model is more exible, yet parsimonious, than several multivariate nonlinear time series models available in the literature. The paper also studies some basic properties of the proposed model, uses a conditional least squares estimation, and proposes a modeling procedure. Finally, we demonstrate applications of the proposed model using simulated and real examples.

Key words and phrases: Hysteresis, least squares estimation, Markov chain, nonlinear model, threshold variable.