What is the function of cointegration theory?

Co-integration theory is mainly used to detect whether there really is an equilibrium dependence between variables, which is very important for establishing an econometric model of non-stationary variables and testing the long-term equilibrium relationship between these variables. Firstly, if multiple nonstationary variables are cointegration, they can be combined into a stationary time series. This stationary time series can be used to describe the equilibrium relationship between the original variables. As long as the equilibrium relationship exists, the stable linear combination between the original variables exists. Secondly, if and only if several non-stationary variables are cointegration, the regression model established by these variables is meaningful. Therefore, cointegration test is also an effective method to distinguish true regression from false regression. Finally, non-stationary variables with cointegration relationship can be used to establish error correction models. Because the error correction model combines long-term relationship and short-term dynamic characteristics in one model, it can not only solve the problem that the traditional econometric model ignores pseudo-regression, but also overcome the weakness of ignoring horizontal variable information when establishing difference model.