Error correction model: Difference between revisions

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An '''error correction model''' belongs to a category of multiple [[time series]] models most commonly used for data where the underlying variables have a long-run stochastic trend, also known as [[cointegration]]. ECMs are a theoretically-driven approach useful for estimating both short-term and long-term effects of one time series on another. The term error-correction relates to the fact that last-periods deviation from a long-run equilibrium, the ''error'', influences its short-run dynamics. Thus ECMs directly estimate the speed at which a dependent variable returns to equilibrium after a change in other variables.

==History of ECM==

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===Engle and Granger 2-step approach===

The first step of this method is to pretest the individual time series one uses in order to confirm that they are [[Stationary process|non-stationary]] in the first place. This can be done by standard [[unit root]] DF testing and [[Augmented Dickey–Fuller test (to test if errors are serially correlated or otherwise)]].

Take the case of two different series <math>x_t</math> and <math>y_t</math>. If both are I(0), standard regression analysis will be valid. If they are integrated of a different order, e.g. one being I(1) and the other being I(0), one has to transform the model.