Must an error correction model be established in cointegration analysis?

In co-integration analysis, there is no need to establish an error correction model, so we can choose according to our needs. If the content of the deleted error correction article is too small, the impulse response or variance decomposition can be increased.

If the time series considered have the same integer order and some linear combination (cointegration vector) reduces the integer order of the combined time series, it is said that there is a significant cointegration relationship between these time series. The so-called cointegration relationship can be understood as a long-term stable relationship between two variables.

In time series, it is often found that there is a long-term stable relationship between two variables, which is called "cointegration relationship". The traditional co-integration analysis method is to transform a long-term stable relationship into a stable sequence through the difference of sequences, and get a linear equilibrium relationship, which can be called linear co-integration. The modeling theory of linear cointegration is to find the possible long-term linear equilibrium relationship in the non-stationary sequence from the actual data generation process to establish the structural model of the sequence! Thus reflecting the operation mechanism of the sequence.