Like PAM we start with static estimator.
The ECM does a regression with first differences, and includes lagged error terms.
We start with a basic first-difference model.
\(\Delta y_t= \Delta x_t\)
We could also expand this to include laggs for both x and y. Here we don’t.
We know that long term \(y_t=\theta x_t\). We use the error from this in a first difference model.
\(\Delta y_t= \alpha \Delta x_t + \beta (y_{t-1}-\theta x_{t-1})\)
Page on identifying error terms
Also, page on Vector Error Correction Model (VECM)