Please excuse me if my question is dumb but I am not a Statistics student. I have a project where I was exploring options for time series analysis where I found some papers on cointegration. I have 4 variables. One of them response variable. I wanted to to the forecasting using the cointegration technique. Please tell me if I am wrong whether the technique to use is a Johansen test. However I understand that the test needs a requirement that the variables are unit root (right?). So I took the software R and did the ADF test in R on each variable (and the first difference ) . But some variables dont pass the adf test. My question is:

  • Is my thinking above right?

  • Then, what do i do for the variables which dont pass the ADF test for unit root ? Can I still take those in the johansen test? If so, what is the purpose of the ADF test at all?

@mpiktas Here I performed the ADF test and here are the results I got:

  • yt.adf Null Hypothesis not rejected (Non Stationary)
  • dyt.adf Null Hypothesis not rejected (Non Stationary)
  • X1t.adf Null hypothesis rejected (Stationary)
  • dX1t.adf Null hypothesis rejected (Stationary)
  • X3t.adf Null hypothesis rejected (Stationary)
  • dX3t.adf Null Hypothesis not rejected (Non Stationary)
  • X4t.adf Null Hypothesis not rejected (Non Stationary)
  • dX4t.adf Null Hypothesis not rejected (Non Stationary)

yt.adf is the response variable while dyt.adf is the firs difference. Similarly other variables. As seen here, I suppose the inference is that none (yt, X1t,X2t,X2t,X4t) are unit root? So then I cant apply johansen test for cointegration,can I?

  • $\begingroup$ Can you be more precise about what you mean by "the cointegration technique"? As far as I know, cointegration is when multiple time series, very roughly, are influenced by a common stochastic process. The Johansen test is a way of testing whether there is cointegration. $\endgroup$
    – Macro
    Commented Jul 20, 2011 at 3:11

1 Answer 1


Johansen test is for testing whether the variables are cointegrated. If they are, the appropriate model is vector error correction model (VECM) which is a special case of vector autoregression models (VAR).

Cointegration is defined for unit root (integrated) time-series. To be more precise a set of variables are said to be cointegrated if their linear combination is stationary. Since any linear combination of stationary time series is stationary the cointegration is specifically defined for non-stationary, i.e. unit root time-series. So yes there is a requirement to test whether the time series in question are unit roots (which by the way is always a good idea if you are using time series in regression).

So to sum up, the answer to your first question is yes, more or less :) It would be good to know how exactly you have determined that ADF test was not passed. It has a lot of variations, and it is easy to make mistakes.

If some of the variables are stationary (did not pass ADF test in your terminology) it is still possible to use VECM. For this however more information is needed about your desired model. If you are only interested in forecasting response variable, simply differencing unit root time series might be sufficient. Then a lot depends whether the response variable is unit root or not. If it is not, then using VECM might not be appropriate.

  • $\begingroup$ I have added some details to the question above... $\endgroup$
    – shishir
    Commented Jul 21, 2011 at 2:09

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