Cointegration

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Cointegration

shishir
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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?
  I am using urca package.
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Re: Cointegration

Arun.stat
As per the definition of co-integration, a system is called co-integrated if that system is integrated (with non zero order) but there exist some linear relationship among the underlying variables which is of order less than "d" (d: the order of the main system.)

Therefore if all your variables are Stationary/Stable then co-integration would not be defined.

In fact for any stationary system, finding a linear stationary relationship is trivial as you are applying some stationary operator on stationary variables. Hence you do not need any fancy testing system to prove/disprove the existance of any such linear relationship.

HTH
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Arun Kumar Saha, FRM
QUANTITATIVE RISK AND HEDGE CONSULTING SPECIALIST
Visit me at: http://in.linkedin.com/in/ArunFRM

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Re: Cointegration

Arun.stat
In reply to this post by shishir
Just to add the answers of your direct questions:

what do i do for the variables which dont pass the ADF test for unit root ?

By definition if some variables are of order "d" and some are of "d1" (d1 < d) then still the system will have order "d". Therefore you can put all your variables into Rank test

what is the purpose of the ADF test at all?

http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test

HTH
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Re: Cointegration

shishir
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That should help me...... Thanks The rank argument makes it amply clear...
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Re: Cointegration

shishir
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Like suggested , I performed the ADF test but 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?