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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 - Y - returns to equilibrium after a change in an independent variable - X. ECMs are 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. • Theoretically-driven approach to estimating time series models.ECMs are useful models when dealing with integrated data, but can also be used with stationary data.
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.
A vector error correction model (VECM) adds error correction features to a multi-factor model such as a vector autoregression model.
Davidson, J.E.H., D.F. Hendry, F. Srba, and J.S. Yeo (1978). Econometric modelling of the aggregate time-series relationship between consumers' expenditure and income in the United Kingdom. Economic Journal, 88, 661-692.
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