8. Threshold Error Correction Model: A Methodological Overview

In this chapter, the methodology related to threshold error correction models is discussed. The aim of the chapter is to summarize several approaches to time series modelling using both a univariate case and a multivariate case. The concept of stationarity is crucial when a model specification is projected. When time series are stationary, then threshold autoregression models or threshold distributed lag models can be estimated. These models represent a framework for flexibly and describe associations showing potentially non-linear and delayed effects in time series data. On the other hand, however, when data exhibit non-stationarity, the non-linear cointegration approach is applied. In this case, the threshold effects around the long run path present in the Threshold Error Correction Model (TECM) are discussed. A modified method for testing for a threshold in TECM based on the Enders and Siklos approach is proposed. Furthermore, methods of statistical inference in the case of a threshold in both stationary and cointegrating spaces are discussed.