[Gretl-users] Test for cointegration

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.