Threshold cointegration: overview and implementation in R

Purpose of this paper is twofold. It is first to offer a rough overview on the field of threshold cointegration, from the seminal paper of Balke and Fomby (1997) to the recent developments. Simultaneously, it is to describe the implementation of the main functionalities for the modeling in the open-source package tsDyn. It provides hence a unique way to get an introduction on the threshold cointegration field allowing in the same time to conduct its own analysis. Introduced by Engle and Granger (1987), the concept of cointegration became a indispensable step in the analysis of non stationary time series. The underlying idea is that even if two variables (or more) are non-stationary, there can exist a combination of them which is stationary. This definition leads to interesting interpretations as the variables can then be interpreted to have a stable relationship (a long-run equilibrium), can be represented in an vector error-correction model, and share a common stochastic trend. However, implicit in the definition is the idea that every small deviation from the long-run equilibrium will lead instantaneously to error correction mechanisms. Threshold cointegration extends the linear cointegration case by allowing the adjustment to occur only after the deviation exceed some critical threshold, thus taking into account possibly transaction costs or stickiness of the prices. Furthermore, it allows to capture asymmetries in the adjustment, where positive or negative deviations won’t be corrected in the same manner.