Error correction model

An error correction model is a dynamical system with the characteristics that the deviation of the current state from its long-run relationship will be fed into its short-run dynamics.

An error correction model is not a model that corrects the error in another model. Error Correction Models (ECMs) are a category of multiple time series models that directly estimate the speed at which a dependent variable——returns to equilibrium after a change in an independent variable—. ECMs are a theoretically-driven approach useful for estimating both short-term and long-term effects of one time series on another. Thus, they often mesh well with our theories of political and social processes. ECMs are useful models when dealing with cointegrated data, but can also be used with stationary data.

Long-run relationship

A rough long-run relationship can be determined by the cointegration vector, and then this relationship can be utilized to develop a refined dynamic model which can have a focus on long-run or transitory aspect such as the two VECM of a usual VAR in Johansen test.