cointegration with different levels of stationary

[mab]

I want to estimate a single model y=f(x1,x2,x3,x4). The y is I(2), xı is (I(0) and others are I(1). What is the wright procedure to estimate in this case? Can anyone explain if johansen cointegration is suitably?

[nayan]

i am also suffering from same problem. could anyone suggest? johansten is used for I(1) or combination of I(1) and I(0) only.
thanks

[samijo]

You might try the book: /Juselius, Katarina. 2006. The Cointegrated VAR Model, Econometric Methodology and Macroeconomic Applications/ which deals with that issue.

[khnaqvi]

In this case you should be using ARDL approach to cointegration as popolarized by Pesaran et al. (2001). This method has the advantage of using it with a mix of variables that are integrated of different degrees.

Hope it works!

Hassan

[tcfoon]

Dear All,

This reply is to correct "Hassan" which is also "khnaqvi" suggestion of the Pesaran et al. (2001) bounds testing to cointegration approach within the Autoregressive Distributed Lag (ARDL) framework in handling the I(2) variables. Yes, the bounds testing to cointegration procedure may use to test the presence of long run equilibrium relationship even when the order of integration is mixture. Nevertheless, this definition is imperfect. Strictly speaking, If the explanatory variables are integrated of order two, I(2), and/or the dependent variable is not I(1) process, then the bounds testing approach cannot be used to determine the existence of cointegrating relations as the critical values provided is only for mixture between I(0) and (1) processes. This is well documented in the published articles used the bounds testing approach. In this sense, we still need to test the degree of integration to ensure that the dependent variable is I(1) and none of the explanatory variables is greater than I(1) process.

To find the presence of cointegration for the case of I(2) variables, the concept of multi-cointegration is useful to us. In addition, it is plausible to check the presence of multi-cointegration within the Engle-Granger two step approach and also Johansen cointegration test. You may refer to Enders (2004) Applied Econometrics Time Series, 2nd Edition for more details.

To "mab", do you serious examined the order of integration for each series under consideration? What do I mean is how many conventional unit root tests you have considered? According to Nelson and Plosser (1982) - Journal of Monetary Economics, most of the macroeconomics variables are I(1) process, however Perron (1989) re-examine the dataset used by Nelson and Plosser (1982) and Perron found that some of the variables is I(0). I suggest you to re-investigate the order of integration before proceed to the next step which is multi-cointegration. Is your unit root test result consistent to the earlier studies? If not do you suspect the validity of your result? Therefore, relying on one statistically approach is not a good guidance for a researcher to make a conclusion for his/her research because nothing is perfect and gap or lack always appear.

Anyway, I hope my suggestion and explanation helpful to you all.

Thank you,

Warmest regards,
tcfoon

[upendar]

I HAVE THE FOLLOWING
y is I(2), xı is (I(0) and X2 IS (1). What is the wright procedure to estimate in this case? Can anyone explain if johansen cointegration is suitably?

[MayankM]

Hello,

I have a problem with the cointegration. I am checking cointegration relationships between three variables which are I(1), I(1) and I(2) respectively. When I ran the Johansen test, it revealed that there is no cointegrating relationship, but it still reports adjustment coefficient and the CE's. Can anybody explain me, why is it so ??

[Wira]

Dear all,
Anybody has Eviews program of ARDL approach cointegration of Pesaran Shin and Smith (2001)?
Would you please share it? Thanks.

[NickyJay]

Only Microfit offers ARDL cointegration. The latest version 5.0 is out now and it's not cheap but from what I've read it offers significant improvements over the previous version. It would be great if EViews could offer the same detailed steps of the ARDL procedure but it would probably take a while to design the necessary code.

[absenadjki]

Dear TC Foon,
Please allow me to express my gratitude on your clear and concise explanation. I made further perusal on your explanations and found affirmative of your suggestions. I will contact you in person for further discussions.

Abdelhak

[lcfreitas]

Thank you all for clarifications on this topic.

An step ahead after the verification of the cointegration of variables with mixed integration orders would be the assessment of the causality relationship of these variables. In this case, considering the presence of cointegration by using the Pesaran bonds tests, would it be possible to draw robust conclusions on Granger causality by employing VECM with variables in different integration order? Has anyone faced this problem?

thank you

[mrduran]

I wrote a simple program to carry out the cointegration test proposed by Pesaran et al. (2001) .
I want to share it with all of you, I hope it will help.

I have two variables which are named t1 and s1 and their 1st differences named dt1 and ds1, but you can modify the least squares equation to include more variables.
s1 is the dependent variable in this setup and there is no intercept term. if you want an intercept, then write
eq.ls ds1 dt1 s1(-1) t1(-1) c ds1(-1 to -!i) dt1(-1 to -!i)
instead of
eq.ls ds1 dt1 s1(-1) t1(-1) ds1(-1 to -!i) dt1(-1 to -!i)

All the information will be written in a matrix named Lags.

HERE THE PROGRAM STARTS (Just copy the rows below and paste it to your eviews program screen)

'create empty equation to be used inside the loop
equation eq

'variable saying how many lags to go up to
!maxlags = 30

''counter of how many equations we have run
!rowcounter=1

'create matrix (named Lags) to store info criteria values, LM test results, error correction coeefficients, t and F test statistics.
matrix(30,15) Lags

for !i=1 to !maxlags
eq.ls ds1 dt1 s1(-1) t1(-1) ds1(-1 to -!i) dt1(-1 to -!i) 'run least squares regression of unrestricted error correction model with lagged values of first differences up to the iTH lag.


'get Akaike, Schwarz and Log Likelihood values for each lag specification and write these numbers to the first three columns of a matrix named "Lags"
Lags(!rowcounter,1) = eq.@aic
Lags(!rowcounter,2) = eq.@schwarz
Lags(!rowcounter,3) = eq.@logl

'get the cointegrating vector (parameter estimates of lagged level variables) and t-stat of the error correction coefficient for each lag specification and write these numbers to the columns 10, 12 and 13 of a matrix named "Lags"
freeze(out) eq
Lags(!rowcounter,10) = @val(out(10,4))
Lags(!rowcounter,12) = @val(out(10,2))
Lags(!rowcounter,13) = @val(out(11,2))

'perform a redundant variables test to acquire the F stat from the restriction of s(-1)=t(-1)=0 for each lag specification and write it to the eleventh column of a matrix named "Lags"
freeze(ftest) eq.testdrop s1(-1) t1(-1)
Lags(!rowcounter,11) = @val(ftest(7,2))
Lags(!rowcounter,15) = @val(ftest(8,2))

d out 'delete tables which are no more needed
d ftest

'perform Breusch-Godfrey LM tests for 1st, 5th and 20th order autocorrelations for each lag specification and write the calculated test statistics along with their respective p-values to the columns 4-9 of a matrix named "Lags"
freeze(lm1) eq.auto(1)
Lags(!rowcounter,4) = @val(lm1(4,2))
Lags(!rowcounter,5) = @val(lm1(4,5))
freeze(lm5) eq.auto(5)
Lags(!rowcounter,6) = @val(lm5(4,2))
Lags(!rowcounter,7) = @val(lm5(4,5))
freeze(lm20) eq.auto(20)
Lags(!rowcounter,8) = @val(lm20(4,2))
Lags(!rowcounter,9) = @val(lm20(4,5))
!rowcounter = !rowcounter+1
d lm1 'delete tables which are no more needed
d lm5
d lm20

next

[azzahra_ipb]

if the ARDL model consists of three variables (a variable dependent (Y) and two variable independent).
Y is I (0) and X 1 is I (1) and X 2 is I (2).
how to estimate this model with eviews??
can somebody help me??.... please

[s.saad.siddiqui]

ARDL
for long term relationship, use below:

Quick
Estimate Equation (LS - Least Squares)
Type: d(y) c d(y(-1)) d(x1) d(x1(-1)) d(x2) d(x2(-1)) y(-1) x1(-1) x2(-1)
Click Ok. Check the results (probs). If ok then click View, Coefficient Tests, Wald
Type Restrictions: c(6)=0, c(7)=0, c(8)=0
If Probability of F Statistic and Chi Square is less than 0.05, it implies existence of long term relation ship.

for short term, i have learnt to to proceed in the same manner and type:
d(y) c d(y(-1)) d(x1) d(x1(-1)) d(x2) d(x2(-1)) ecm OR
d(y) c d(y(-1)) d(x1) d(x1(-1)) d(x2) d(x2(-1)) ect(-1)

but, unfortunately some error occurs where ecm or ect is not considered as defined.

all are requested to please advise on correctness of ARDL short run equation stated above.

[bvguizar]

http://www.youtube.com/watch?v=d9E8BKsocis&feature=plcp

Someone that can help me please

I have a question! In articles authors express ARDL model by using just lag values of independent variables plus differences of them. But in your model, you use t values of explanatory variables instead of t-1. Why? And how can I establish by using lag values of explanatory variables in microfit? Thank you in advanced. Blanca! York PhD!!!
[My model is y y(-1) x(-1) z(-1) d(y(-1)) d(x(-1)) d(z(-1))]