Stability Of Regime Switching Error Correction Models Under Linear Cointegration

The paper obtains conditions that ensure stationarity of linear long-run equilibrium relations and differenced observations in vector autoregressive error correction models with nonlinear short-run dynamics. The considered models include various threshold error correction models and their smooth transition counterparts. These models assume that the form of the short-run dynamics depends on values of observable transition functions that determine the regime in which the considered process evolves. In related models studied in the paper the transition functions are unobservable. These models are obtained by making the transition functions of threshold error correction models dependent on an unobservable random term. Previous stationarity conditions obtained for these kinds of regime switching error correction models are extended by using recent developments on nonlinear autoregressive models based on the theory of Markov chains and the concept of joint spectral radius of a set of square matrices. In addition to stationarity, existence of second-order moments and beta mixing is also established. The results of the paper enhance the understanding of the considered nonlinear error correction models and pave the way for the development of their asymptotic estimation and testing theory.Financial support from the Research Unit of Economic Structures and Growth (RUESG) in the University of Helsinki and the Yrjö Jahnsson Foundation is gratefully acknowledged. The author thanks Anders Rahbek for stimulating discussions on the topic of this paper and Helmut Lütkepohl and an anonymous referee for useful comments.