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.
Title: 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.
