Many texts (e.g. Hayashi (2002), Econometrics, Princeton University Press, from page 644) give a fuller account of this test than would be possible in a forum such as this. I would have several questions. If your series are oil prices should you have a trend in your unit root tests. The critical values for the residual based test of cointegration are different from those for unit value tests. If they are oil prices it is possible that there is more than one cointegration relationship and the Johansen procedure might be more appropriate.
The economic theory on which your assumption of cointegration is based is important in determining cointegration. Best regards John On 27 July 2010 16:40, Farmer, Jesse <Jesse.Farmer(a)kochind.com> wrote: > 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 > -- John C Frain Economics Department Trinity College Dublin Dublin 2 Ireland www.tcd.ie/Economics/staff/frainj/home.html mailto:frainj(a)tcd.ie mailto:frainj(a)gmail.com
