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 > in advance. > > Thanks! > > 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. Allin Cottrell
