# Error Correction Model for p=1?

When building an Error Correction Model, is there any point in keeping p=1? I see a lot of equations where there t is influenced not only by t-1 but also t-2. If I only have t-1, is it useful at all to use the VECM framework? Or should I use a different framework? Initially I looked into it to address the non stationarity in my dataset.

• Could you include an equation to illustrate what you mean? In the standard setting, including more than one lagged error corrections terms will cause perfect multicollinearity. Aug 26, 2016 at 19:17

• theoretical considerations (e.g. you need a model that includes lag $p$ if you want to test a hypothesis associated with some coefficient of lag $p$).
A VECM is flexible in terms of lag length as technically you can specify any lag length greater or equal to zero. There is no need to always stick to $p=1$ as in your example.
Note that the error correction term is included only once, typically with lag 1 or lag $p$. Including error correction term more than once (with different lags) will result in perfect multicollinearity in the model.