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The second step is then to estimate the model using [[Ordinary least squares]]: <math> y_t = \beta_0 + \beta_1 x_t + \epsilon_t </math>
If the regression is not spurious as determined by test criteria described above, [[Ordinary least squares]] will not only be valid, but in fact super [[consistent estimator|consistent]] (Stock, 1987).
Then the predicted residuals <math>\hat{\epsilon_t}= y_t -\beta_0 - \beta_1 x_t </math> from this regression are saved and used in a regression of differenced variables plus a lagged error term: <math> A(L) \Delta y_t = \gamma + B(L)\Delta x_t + \alpha \hat{\
One can then test for cointegration using a standard [[t-statistic]] on <math>\alpha</math>.
While this approach is easy to apply, there are, however numerous problems:
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