From
Hansen, B., Threshold autoregression in economics. Statistics and Its Interface, 2011. 4(2): p. 123--128.

Balke and Fomby [ 7] introduced a “threshold cointe-gration” multivariate model which allows a discontinuous adjustment to long-run equilibrium. It is a combination of Tong’s TAR model and Engle and Granger’s model of cointegration [30] known as a vector error-correction model (VECM). The threshold cointegration model has been enor-mously influential in economics. Tsay [77] introduced a sim-ilar vector TAR (VTAR) model with possible threshold cointegration. Enders and Siklos [28] extended the Engle-Granger test for cointegration to allow for threshold adjust-ment. Estimation methods for the threshold VECM model were developed by Hansen and Seo [45], who also develop tests for the presence of threshold effects within the thresh-old VECM. Gonzalo and Pitarakis [ 33] develop similar tests in the context of a single cointegrating regression. Seo [ 71] develops a test for the null of no cointegration against the alternative of threshold cointegration. Seo [73] develops an asymptotic distribution theory for the estimates of the coin-tegration vector in the threshold VECM model.