The Theoretical And Empirical Research Of Threshold Cointegration Based On The Equilibrium-Deviation Term

Since Engles and Granger (1987) put forwards the concept of cointegration, the cointegration theory has helped economists to extend their view on the long-term equilibrium relationship of many non-stationary economic and financial time series. This traditional cointegration theory assumes the adjustment paths towards equilibrium to be continuous. However, recent studies show that many important time series do not actually follow such an assumption because of the existence of fixed adjustment cost or policy interventions. Instead, they either do no adjustment until the deviation from the equilibrium exceeds a critical threshold or adjust in unequal paces in different intervals. In such a case, statistic inference methods in traditional cointegration theory are no longer valid.To solve this problem, the threshold cointegration theory was developed. In this theory, a set of threshold autoregression models are used to precisely describe the time series with discontinuous adjustment paths. There are two key points to study. One is the estimation of threshold and the test for the presence threshold. And the other key point comes from the invalidity of traditional unit root tests and cointegration tests. A set of unit root tests and cointegration tests in the context of threshold effect are developed with significant higher test power. According to the research frame, existing studies are divided into two types. One is based on the equilibrium-deviation term, and the other is in the threshold vector error-correction mechanism (TVECM) model.This paper is expanded on the equilibrium-deviation term. First of all, the characteristics of some threshold autoregression models are analyzed; then, a comparison between two threshold estimation methods, arranged autoregressive method and grid search method, is done by Monte Carlo experiment with a conclusion that grid search method performs better in small sample cases; thirdly, and as the key part of this paper, a residual-based block bootstrap is implemented to construct a sup-Wald statistic for both a unit root test in the context of threshold effect and the test for the presence of threshold. In the finite sample performance analysis, the sup-Wald test is proved to have higher test power than traditional ADF test; last but not the least, an empirical investigation on the term structure of interest rates is done, strong evidences of threshold effect are found.