Hello:

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 in advance.

Thanks!

My output below:
-----------------

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

   test with constant
   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
   1st-order autocorrelation coeff. for e: 0.004
   lagged differences: F(5, 510) = 7.952 [0.0000]
   estimated value of (a - 1): -0.00320084
   test statistic: tau_c(1) = -1.10968
   asymptotic p-value 0.7144

Step 2: testing for a unit root in Var2

Augmented Dickey-Fuller test for Var2
including 5 lags of (1-L)base
sample size 517
unit-root null hypothesis: a = 1

   test with constant
   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
   1st-order autocorrelation coeff. for e: 0.001
   lagged differences: F(5, 510) = 2.011 [0.0756]
   estimated value of (a - 1): -0.00202185
   test statistic: tau_c(1) = -0.612473
   asymptotic p-value 0.8656

Step 3: testing for a unit root in Var3

Augmented Dickey-Fuller test for Var3
including 5 lags of (1-L)peak
sample size 517
unit-root null hypothesis: a = 1

   test with constant
   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
   1st-order autocorrelation coeff. for e: 0.002
   lagged differences: F(5, 510) = 2.565 [0.0263]
   estimated value of (a - 1): -0.0015613
   test statistic: tau_c(1) = -0.535532
   asymptotic p-value 0.8819

Step 4: testing for a unit root in Var4

Augmented Dickey-Fuller test for Var4
including 5 lags of (1-L)nbp
sample size 517
unit-root null hypothesis: a = 1

   test with constant
   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
   1st-order autocorrelation coeff. for e: 0.001
   lagged differences: F(5, 510) = 5.671 [0.0000]
   estimated value of (a - 1): -0.0011618
   test statistic: tau_c(1) = -0.431389
   asymptotic p-value 0.9016

Step 5: testing for a unit root in Var5

Augmented Dickey-Fuller test for Var5
including 5 lags of (1-L)brent
sample size 517
unit-root null hypothesis: a = 1

   test with constant
   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
   1st-order autocorrelation coeff. for e: 0.001
   lagged differences: F(5, 510) = 1.759 [0.1196]
   estimated value of (a - 1): -0.00386803
   test statistic: tau_c(1) = -1.05127
   asymptotic p-value 0.7369

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 ***

Mean dependent var   109.5593   S.D. dependent var   35.61656
Sum squared resid    16623.86   S.E. of regression   5.665015
R-squared            0.974895   Adjusted R-squared   0.974701
Log-likelihood      -1646.637   Akaike criterion     3303.274
Schwarz criterion    3324.571   Hannan-Quinn         3311.615
rho                  0.946380   Durbin-Watson        0.103074

Step 7: testing for a unit root in uhat

Augmented Dickey-Fuller test for uhat
including 5 lags of (1-L)uhat
sample size 517
unit-root null hypothesis: a = 1

   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
   1st-order autocorrelation coeff. for e: -0.001
   lagged differences: F(5, 511) = 3.361 [0.0054]
   estimated value of (a - 1): -0.0533006
   test statistic: tau_c(5) = -3.60562
   asymptotic p-value 0.2762

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.