First do the unit root test to see if the variable sequence is stationary. If it is stationary, you can construct a classical econometric model such as regression model; if it is not stationary, perform the difference. (Note that the trend and intercept are selected in different situations, and are determined according to the P value and the original hypothesis). If all test sequences obey the same-order single integration, a VAR model can be constructed, and a co-integration test can be done (pay attention to the choice of lag period) to determine whether there is a co-integration relationship between the variables within the model, that is, whether there is a long-term equilibrium relationship. If so, the VEC model can be constructed or the Granger causality test can be performed to test the "who caused who changed" between the variables, that is, the causal relationship.
1. Stationarity problem
The unit root test is the stationarity test of the series. If the stationarity of the series is not tested, direct OLS will easily lead to false regression.
When the data to be tested is stationary (that is, there is no unit root), to further examine the causal relationship of variables, the Granger causality test can be used, but the premise of the Granger test is that the data must be stationary, otherwise it cannot be Do.
When the tested data is non-stationary (that is, there is a unit root), and each sequence is single-integration of the same order (the premise of co-integration test), if you want to further determine whether there is a co-integration relationship between variables, you can perform co-integration test, co-integration test There are mainly EG two-step method and JJ test:
A. The EG two-step method is based on the test of regression residuals, and the stationarity of the residuals can be tested by establishing an OLS model (generally, the EG two-step method is used)
B. The JJ test is a test based on regression coefficients, provided that a VAR model is established (that is, the model conforms to the ADL model)
When there is a co-integration relationship between variables, ECM can be established to further examine the short-term relationship. Eviews also provides a Wald-Granger test, but the Granger test at this time is not a causal relationship test, but a variable exogenous test. Please Pay attention to identification
2. Cointegration problem
Granger's test can only be used for stationary series! This is the premise of the Granger test, and its causal relationship is not the relationship between cause and effect as we usually understand, but that the previous change of x can effectively explain the change of y, so it is called "Granger cause".
Non-stationary series are likely to appear pseudo-regression. The significance of cointegration is to test whether the causal relationship described by their regression equation is pseudo-regression, that is, to test whether there is a stable relationship between variables. Therefore, the causality test for non-stationary series is the cointegration test.
The stationarity test has 3 functions: 1) Test the stationarity, if it is stable, do the Granger test, if it is not stationary, it is a positive test. 2) The single integer order of each sequence is used in the cointegration test. 3) Judging the data generation process of the time column.
3. Granger causality problem
In fact, many people have misunderstandings. The following points need to be clarified:
First, the Granger causality test is to test the chronological order of statistics, and it does not mean that there is a causal relationship. Whether it is a causal relationship needs to be determined according to theory, experience and models.
Second, the variables of the Granger causality test should be stationary. If the unit root test finds that the two variables are unstable, then the Granger causality test cannot be performed directly. Therefore, many people test the unstable variables. Ranger causality test, which is wrong.
Third, the cointegration result only indicates that there is a long-term equilibrium relationship between variables. Then, should we do Granger first or do cointegration first? Cointegration is required because the variables are not stationary. Therefore, firstly, the variables are differentiated. After they are stationary, the Granger causality test can be used to determine the sequence of variable changes. Then, cointegration is performed to see if the variables exist. long-run equilibrium.
Fourth, long-term equilibrium does not mean the end of the analysis, and short-term fluctuations should also be considered, and an error correction test should be done.
First do the unit root test to see if the variable sequence is stationary. If it is stationary, you can construct a classical econometric model such as regression model; if it is not stationary, perform the difference. (Note that the trend and intercept are selected in different situations, and are determined according to the P value and the original hypothesis). If all test sequences obey the same-order single integration, a VAR model can be constructed, and a co-integration test can be done (pay attention to the choice of lag period) to determine whether there is a co-integration relationship between the variables within the model, that is, whether there is a long-term equilibrium relationship. If so, the VEC model can be constructed or the Granger causality test can be performed to test the "who caused who changed" between the variables, that is, the causal relationship.
1. Stationarity problem
The unit root test is the stationarity test of the series. If the stationarity of the series is not tested, direct OLS will easily lead to false regression.
When the data to be tested is stationary (that is, there is no unit root), to further examine the causal relationship of variables, the Granger causality test can be used, but the premise of the Granger test is that the data must be stationary, otherwise it cannot be Do.
When the tested data is non-stationary (that is, there is a unit root), and each sequence is single-integration of the same order (the premise of co-integration test), if you want to further determine whether there is a co-integration relationship between variables, you can perform co-integration test, co-integration test There are mainly EG two-step method and JJ test:
A. The EG two-step method is based on the test of regression residuals, and the stationarity of the residuals can be tested by establishing an OLS model (generally, the EG two-step method is used)
B. The JJ test is a test based on regression coefficients, provided that a VAR model is established (that is, the model conforms to the ADL model)
当变量之间存在协整关系时，可以建立ECM进一步考察短期关系，Eviews这里还提供了一个Wald－Granger检验，但此时的格兰杰已经不是因果关系检验，而是变量外生性检验，请注意识别
2. 协整问题
格兰杰检验只能用于平稳序列！这是格兰杰检验的前提，而其因果关系并非我们通常理解的因与果的关系，而是说x的前期变化能有效地解释y的变化，所以称其为“格兰杰原因”。
非平稳序列很可能出现伪回归，协整的意义就是检验它们的回归方程所描述的因果关系是否是伪回归，即检验变量之间是否存在稳定的关系。所以，非平稳序列的因果关系检验就是协整检验。
平稳性检验有3个作用：1）检验平稳性，若平稳，做格兰杰检验，非平稳，作协正检验。2）协整检验中要用到每个序列的单整阶数。3）判断时间学列的数据生成过程。
3. 格兰杰因果问题
其实很多人存在误解。有如下几点，需要澄清：
第一，格兰杰因果检验是检验统计上的时间先后顺序，并不表示而这真正存在因果关系，是否呈因果关系需要根据理论、经验和模型来判定。
第二，格兰杰因果检验的变量应是平稳的，如果单位根检验发现两个变量是不稳定的，那么，不能直接进行格兰杰因果检验，所以，很多人对不平稳的变量进行格兰杰因果检验，这是错误的。
第三，协整结果仅表示变量间存在长期均衡关系，那么，到底是先做格兰杰还是先做协整呢？因为变量不平稳才需要协整，所以，首先因对变量进行差分，平稳后，可以用差分项进行格兰杰因果检验，来判定变量变化的先后时序，之后，进行协整，看变量是否存在长期均衡。
第四，长期均衡并不意味着分析的结束，还应考虑短期波动，要做误差修正检验。