Hi guys,
I tried the Engle-Granger cointegration test but I noticed something. Here
is my procedure:
1.I estimated a equatation in cointegration dialogue with the following
variables l_CPI, l_REER, MMR and l_Y using 12 lags and got these results
down.
2. These ADF tests for these variables are wright and the results are the
same if you do ADF tests through main Gretl window using the same number of
lags.
3.In step 5 we have the cointegration results and they are the same if you
estimate a OLS model through main Gretl window.
4.In step 6 we have ADF tests for the residuals. Tests are without a
constant. I tried to check the same test through main Gretl window using the
same specification ie. I saved residuals from OLS regression (which I done
through the main Gretl window) and tested with the ADF test without a
constant. Here are the results:
From Engle-Granger cointegration:
Step 6: Dickey-Fuller test on
residuals
Augmented Dickey-Fuller tests, order 12, for uhat
sample size 86
unit-root null hypothesis: a = 1
test without constant
estimated value of (a - 1): -0,333671
test statistic: t = -2,46579
asymptotic p-value 0,4903
From maing Gretl window:
Augmented Dickey-Fuller tests, order
12, for uhat
sample size 86
unit-root null hypothesis: a = 1
test without constant
model: (1 - L)y = (a-1)*y(-1) + ... + e
estimated value of (a - 1): -0,333671
test statistic: t = -2,46579
asymptotic p-value 0,01324
Test statistics and estimated values, sample size are the same, but p-values
are different?
From the first test ie. E-G one could conclude that there is no
cointegration and from the second (from OLS saved residuals) that there is a
cointegration relationship.
Why is that?
Did I make same mistaque in comparing?
In addition I have some one suggestion. There sould be a possibility in E-G
cointegration to have a possibility to do ADF tests-test down from maximal
lag order or to have a possibility to see full ADF tests output in automatic
E-G cointegration procedure. With unique lag order specification one can't
decide which is the wright lag order.
***********************************
Step 1: testing for a unit root in l_CPI
Augmented Dickey-Fuller tests, order 12, for l_CPI
sample size 86
unit-root null hypothesis: a = 1
test with constant
estimated value of (a - 1): -0,0107669
test statistic: t = -1,2609
asymptotic p-value 0,6499
with constant and trend
estimated value of (a - 1): -0,0838183
test statistic: t = -2,51286
asymptotic p-value 0,3218
with constant and quadratic trend
estimated value of (a - 1): -0,111113
test statistic: t = -1,86159
asymptotic p-value 0,8653
Step 2: testing for a unit root in l_REER
Augmented Dickey-Fuller tests, order 12, for l_REER
sample size 86
unit-root null hypothesis: a = 1
test with constant
estimated value of (a - 1): -0,0393688
test statistic: t = -1,28046
asymptotic p-value 0,641
with constant and trend
estimated value of (a - 1): -0,244764
test statistic: t = -4,98476
asymptotic p-value 0,0001
with constant and quadratic trend
estimated value of (a - 1): -0,132398
test statistic: t = -1,67802
asymptotic p-value 0,9135
Step 3: testing for a unit root in MMR
Augmented Dickey-Fuller tests, order 12, for MMR
sample size 86
unit-root null hypothesis: a = 1
test with constant
estimated value of (a - 1): -0,0881019
test statistic: t = -1,97264
asymptotic p-value 0,2992
with constant and trend
estimated value of (a - 1): -0,137154
test statistic: t = -2,13296
asymptotic p-value 0,5267
with constant and quadratic trend
estimated value of (a - 1): -0,263064
test statistic: t = -2,29448
asymptotic p-value 0,6817
Step 4: testing for a unit root in l_Y
Augmented Dickey-Fuller tests, order 12, for l_Y
sample size 86
unit-root null hypothesis: a = 1
test with constant
estimated value of (a - 1): 0,0899723
test statistic: t = 1,56751
asymptotic p-value 0,9995
with constant and trend
estimated value of (a - 1): -1,13912
test statistic: t = -3,52897
asymptotic p-value 0,0363
with constant and quadratic trend
estimated value of (a - 1): -1,06705
test statistic: t = -2,83268
asymptotic p-value 0,3813
Step 5: cointegrating regression
Cointegrating regression -
OLS estimates using the 99 observations 1998:01-2006:03
Dependent variable: l_CPI
VARIABLE COEFFICIENT STDERROR T STAT P-VALUE
const 5,03993 0,562006 8,968 <0,00001 ***
l_REER -0,305748 0,0911986 -3,353 0,00115 ***
MMR -0,0121330 0,00102131 -11,880 <0,00001 ***
l_Y 0,225401 0,0419834 5,369 <0,00001 ***
Unadjusted R-squared = 0,845111
Adjusted R-squared = 0,840219
Durbin-Watson statistic = 0,633496
First-order autocorrelation coeff. = 0,668083
Step 6: Dickey-Fuller test on residuals
Augmented Dickey-Fuller tests, order 12, for uhat
sample size 86
unit-root null hypothesis: a = 1
test without constant
estimated value of (a - 1): -0,333671
test statistic: t = -2,46579
asymptotic p-value 0,4903
P-values based on MacKinnon (JAE, 1996)
There is evidence for a cointegrating relationship if:
(a) The unit-root hypothesis is not rejected for the individual variables.
(b) The unit-root hypothesis is rejected for the residuals (uhat) from the
cointegrating regression.
Augmented Dickey-Fuller tests, order 12, for uhat
sample size 86
unit-root null hypothesis: a = 1
test without constant
model: (1 - L)y = (a-1)*y(-1) + ... + e
estimated value of (a - 1): -0,333671
test statistic: t = -2,46579
asymptotic p-value 0,01324
P-values based on MacKinnon (JAE, 1996)
_________________________________________________________________
Windows Live Messenger has arrived. Click here to download it for free!
http://imagine-msn.com/messenger/launch80/?locale=en-gb