Re: [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. _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users