In macroeconomic econometric analysis, the cointegration method proposed by Granger (1987) has become one of the most important tools to analyze the quantitative relationship between non-stationary economic variables, and the linear adjustment mechanism between economic variables is described by the linear error correction model (ECM), which is called the linear cointegration method.
With the development of economic theory, especially in the economic analysis of transaction costs and policy responses, the traditional linear cointegration analysis is no longer an appropriate analysis method. In view of this, Balk and Fomby( 1997)? [ 1]? The so-called threshold cointegration method is proposed to describe the nonlinear adjustment mechanism between economic variables.
Purpose:
Co-integration means that there is a random trend of * * *. The purpose of cointegration test is to determine whether the linear combination of a group of non-stationary sequences has a stable equilibrium relationship. A special case of pseudo-regression is that the trend components of two time series are the same, and this * * * same trend correction regression may make it reliable.
It is precisely because cointegration conveys a long-term equilibrium relationship. If a reliable relationship can be found between several variables that seem to have a single random trend, then by introducing this "relative stationarity" to adjust the model, the random trend brought by the unit root can be eliminated, which is the so-called error correction model.
In time series analysis, it is traditionally required that the time series used must be stable, that is, there is no random trend or definite trend, otherwise the problem of "pseudo-regression" will appear. However, in the real economy, the time series is usually non-stationary, and we can make it stable by difference, but this will make us lose the long-term information of the total, which is necessary for analyzing the problem, so we use cointegration to solve this problem.