Time-Series – Analyzing VAR with Trend-Stationary Variables

cointegrationstationaritytime seriestrendvector-autoregression

I'm currently trying to estimate a VAR with 3 variables – consumption, investment and a credit spread. I have inspected the variables and run ADF tests to determine that they are in-fact trend-stationary rather than processes with a unit root. On running a Johansen test to check if they cointegrate, I find that the LR equilibrium matrix has a rank of 1. I have 2 questions:

  1. Does it make sense to run a cointegration test on trend stationary variables?
  2. In order to estimate the VAR, should I detrend the variables and use the detrended data in my estimation?

Any help would be much appreciated!

Best Answer

  1. No, it does not make sense to run a cointegration test on trend stationary variables. Cointegration requires variables with unit roots.
  2. You can either detrend the variables beforehand or include a trend in the VAR model as an exogenous regressor.
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