Stationarity and Co-Integration

[gobbble]

Hi together, I have some questions about the right modeling.

I have time series data and my regression looks like follows

Y c X1 X2t-1 X3t-1 X4

My variables are integrated in order 0,1 and 2 like follows:

Y, X1, X2, = I(0)
X3 = I(1)
X4 = I(2)

What is now the right approach?

a) Do I take the first difference of variable X3 and second difference of X4 to assume stationarity so that my regression looks like:
Y c X1 X2t-1 d(X3t-1) d(X4,2)

b) or do I simply include an ar(1) term like

Y c X1 X2t-1 X3t-1 X4 ar(1)

c) or do I include both like

Y c X1 X2t-1 d(X3t-1) d(X4,2) ar(1)


My second question would be regarding co-integration. To make my anlaysis more interesting I would like to do co-integration analysis and granger causality.

As far as I am concerned, the Johansen co-integration approach can just be conducted with variables integrated in the same oder (order of 1 or more). But my dependent variable is I(0). Is there a way to do the co-integration test anyway?

I read here http://forums.eviews.com/viewtopic.php? ... ardl#p3390 about an ADRL approach but I do not reall get it.



Thank you very much in advance for your help

[gobbble]

Can no one help me ? :(

I will post my workfile to illustrate my problem.

All variables are I(0) except of

CH_UKREAL, RS_UKREAL & GBP_RUB which are I(1)
and

GBP_CNY & GBP_HKD which are I(2)

Art is always my dependet variable and crisis is a dummy variable

I want to check the influence of the different countries in individual and aggregate form on art.

So for instance, my initial OLS regression (=CHINALAG) for China on art was

ART c GBP_CNY CH_UKREAL(-1) CRISIS

To account for stationarity I modified it to (=CHINALAGDIFF)

ART c D(GBP_CNY,2) D(CH_UKREAL(-1)) CRISIS
Is that the right apporach????

As you can see from the regression outputs, the significances disappeared in the second model and the adjusted R^2 is smaller. In addition DW statistic does look worse , so I doubt that my approach was right.

I really would appreciate you help.

• Have I done the modeling right?
• Should I add AR(1) instead (or in addition) to the differences?
• Is there a way to apply cointegration on art even though the variables are integrated in different order?

Thanks a lot in advance. I hope someone is willing to help me here.

[gobbble]

still wondering...

[Siewwen]

I hope someone responds to your question on the differencing of terms for your model, because I'm having the same problem myself! My y variable is I(0) but x variables a variant of I(1) and I(2) terms.

With regard to Johansen, why would you want to include y in the test since it is I(0) and therefore stationary? I thought what would be interesting is the long run relationship between your I(1) and I(2) variables which are non-stationary, in which case you can do a Johansen by converting your I(2) variable into I(1) by using genr dx = d(x,1) and the running dx and the other I(1) in Johansen.

Hope someone can confirm this and the model specification question please, I'm a beginner in econometrics and would appreciate help from more advanced folks. Thanks!

[gobbble]

Hi Siewwen,

thanks for your reply.
Regarding the model, I think the right approach is to include all variables with the neccessary differences as soon as it is economically considereable, so this one
ART c D(GBP_CNY,2) D(CH_UKREAL(-1)) CRISIS
should be the right one.

To include as ar(1) model is just useful if you have autocorrelation. In reference to what startz is saying (http://forums.eviews.com/viewtopic.php?f=4&t=1289), autocorrelation on individual level can be disregarded, just the final regression must no be autocorrelated. If that is the case, one might want to add an ar(1) term.

I am still wondering about the purpose of the Cointegrationt test. If you are runing an OLS with differenced variables yoz are checking on co-movement. If you do the Co-integration test, on I(1) level variables, you check on co-integration. Where exactley is the difference?

I am also wondering how to interprete the Johansen Cointegrationr results.
What is the conclusion, if I can reject the H0 in all rows like indicated in the attached file.

If I can reject both, that there is no cointegration, and that there is at most one cointegration vector (two variables). Is it inconclusive? Or can I conclude that there are one or more cointegration vectors, even though I have only 2 variables? I am abit puzzled here

[gobbble]

To state the question simple, is it possible for two variables to have two cointegraded relations?
Or can I derive no conclusions from the test results at hand?