Co-integration test determines 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. At this time, you can use this * * * same direction correction regression to make it reliable. In the real economy, 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.

And this information is necessary to analyze the problem, so cointegration is used to solve this problem. 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.

Extended data

Through the simulation study of test statistics, the research shows that the statistics of fixed regression element self-help method have high test potential in testing so-called partial cointegration and M- partial cointegration, but the fixed regression element self-help method has serious lateral distortion in testing partial cointegration and M- partial cointegration, and both of them will increase the probability of "discarding truth".

However, when the simulation threshold is used to test the level simulation, the horizontal distortion is small; Secondly, with the continuous enhancement of data sequence, the test potential will decrease, but the decline rate is not as fast as that of EG two-step method. The third test method of simulated critical value has lower test potential when testing M- partial cointegration than when testing partial cointegration.

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