On Tue, 27 Jul 2010, Farmer, Jesse wrote:
I am doing a test for cointegration across 5 time-series variables.
I've run the test but I am not sure how to interpret the output. Could
someone tell me if my data is exhibiting cointegration, and if so, how
did you determine that? I realize this is a n00b question, so apologies
My output below:
[output edited for brevity]
Step 1: testing for a unit root in Var1
Augmented Dickey-Fuller test for Var1
including 5 lags of (1-L)api2
sample size 517
unit-root null hypothesis: a = 1
asymptotic p-value 0.7144
Large p-value: unit root not rejected for Var1.
Step 2: testing for a unit root in Var2
Augmented Dickey-Fuller test for Var2
asymptotic p-value 0.8656
Nor for Var2.
Step 3: testing for a unit root in Var3
Augmented Dickey-Fuller test for Var3
asymptotic p-value 0.8819
Nor for Var3.
Step 4: testing for a unit root in Var4
Augmented Dickey-Fuller test for Var4
asymptotic p-value 0.9016
Var4 the same.
Step 5: testing for a unit root in Var5
Augmented Dickey-Fuller test for Var5
asymptotic p-value 0.7369
And Var5 the same. It's possible to conclude that all 5 series are
non-stationary (have unit roots) considered individually, based on
these tests. Now...
Step 6: cointegrating regression
Cointegrating regression -
OLS, using observations 2008/01/02-2010/01/01 (T = 523)
Dependent variable: api2
coefficient std. error t-ratio p-value
const -35.8323 1.81277 -19.77 3.20e-065 ***
base 1.58498 0.321094 4.936 1.08e-06 ***
peak -0.701765 0.225461 -3.113 0.0020 ***
nbp 0.848089 0.0617052 13.74 7.18e-037 ***
brent 0.686534 0.0279061 24.60 4.14e-089 ***
Step 7: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
asymptotic p-value 0.2762
The p-value here is smaller than for the individual series, but
still not very small. For clear evidence of cointegration you're
looking for a fairly decisive rejection of the unit-root null at
this point (say, a p-value less than .05), but you ain't got it!
You might try the Johansen procedure (gretl's "coint2" command)
and see if that tells you anything different.