1. Determine the variable

You need to determine the variables to study. Usually, it is necessary to study the relationship between two or more variables. For example, to study the relationship between stock price and interest rate, we need to determine these two variables.

2. Carry out unit root test

Next, you need to test the unit root. Unit root test is used to test whether the time series has a unit root, that is, whether it has the characteristics of random walk. If the time series has a unit root, it is non-stationary and cannot be tested by cointegration. The commonly used unit root test methods are ADF test and Phillips-Perron test.

3. Cointegration test

If the variables are found to be stable after the unit root test, then the cointegration test can be carried out. Cointegration test is used to test whether there is a long-term relationship between two or more variables. Commonly used cointegration test methods include Engle-Granger test and Johansen test.

4. Analyze the error correction model (ECM).

If the co-integration test results show that there is a long-term relationship between variables, then the error correction model (ECM) analysis can be carried out. ECM model is used to describe the short-term dynamic relationship between variables. ECM model includes long-term equilibrium relationship and short-term adjustment mechanism. Through ECM model, we can study the short-term and long-term relationship between variables.

Cointegration test is a method used to study the relationship between time series. Through cointegration test, we can judge whether there is a long-term relationship between variables and analyze the error correction model. In the financial field, cointegration test is often used to study the relationship between stock prices, exchange rates, interest rates and other variables.