Vector Error Correction – Understanding Order of Integration in Vector Error Correction Models

cointegrationrunit rootvector-error-correction-model

I am trying to estimate VEC models for three variables in different regions. So, using each region's data I am estimating a different VEC model. Mostly, series are I(1) and co-integrated. To have uniformity I want to stick with the class of models. However, in some regions I have some series as I(0) and I(2). My questions are:

  1. When a series is I(0), can I do cumulative sum (opposite of differencing) and check whether that is I(1) and proceed with fitting the model if it is I(1) now?

  2. When a series is I(2), can I difference it once and fit the model?

I am using DF-GLS test to check for order of integration. Specifically ur.ers() function in urca package of R. Also, mostly when the variable is I(0) according to DF-GLS, KPSS test still indicates the series to be I(1).

Side question: is there a way to check for stability of VEC models in R.

Thanks in advance

Best Answer

  1. If a series is I(0), then its cumulative sum is I(1) by definition. So if you trust the premise, there is no need to check the implication empirically.
  2. If there is a single I(2) series in the system while the other ones are I(1) or I(0), it is fine to difference the I(2) series. If there are more than one I(2) series, they may be cointegrated, and that should be checked out as the first step.
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