| 27.34 | 11.52 |
| 29.41 | 12.28 |
| 29.53 | 12.07 |
| 29.63 | 11.89 |
| 30.09 | 12.06 |
| 29.93 | 12.04 |
| 29.8 | 12.12 |
| 28.81 | 11.63 |
| 30.15 | 12.36 |
| 29.38 | 12.06 |
| 28.56 | 11.91 |
| 28.02 | 11.51 |
The coint gives below
? coint 1 v1 v2
Step 1: testing for a unit root in v1
Augmented Dickey-Fuller test for v1
including one lag of (1-L)v1
sample size 10
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: -0.038
estimated value of (a - 1): -0.547219
test statistic: tau_c(1) = -0.9848
asymptotic p-value 0.7608
Step 2: testing for a unit root in v2
Augmented Dickey-Fuller test for v2
including one lag of (1-L)v2
sample size 10
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: -0.636
estimated value of (a - 1): -2.03223
test statistic: tau_c(1) = -2.51525
asymptotic p-value 0.1118
Step 3: cointegrating regression
Cointegrating regression -
OLS, using observations 2116-2127 (T = 12)
Dependent variable: v1
coefficient std. error t-ratio p-value
-------------------------------------------------------
const -2.51980 6.46980 -0.3895 0.7051
v2 2.65519 0.541085 4.907 0.0006 ***
Mean dependent var 29.22083 S.D. dependent var 0.872108
Sum squared resid 2.454878 S.E. of regression 0.495467
R-squared 0.706575 Adjusted R-squared 0.677233
Log-likelihood -7.506284 Akaike criterion 19.01257
Schwarz criterion 19.98238 Hannan-Quinn 18.65351
rho 0.519235 Durbin-Watson 0.745625
Step 4: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including one lag of (1-L)uhat
sample size 10
unit-root null hypothesis: a = 1
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: -0.094
estimated value of (a - 1): -0.676281
test statistic: tau_c(2) = -2.36751
asymptotic p-value 0.34
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.
Manually do a adf on the $uhat of the v1 const v2 but the output is different from the coint
output
? ols v1 const v2
Model 8: OLS, using observations 2116-2127 (T = 12)
Dependent variable: v1
coefficient std. error t-ratio p-value
-------------------------------------------------------
const -2.51980 6.46980 -0.3895 0.7051
v2 2.65519 0.541085 4.907 0.0006 ***
Mean dependent var 29.22083 S.D. dependent var 0.872108
Sum squared resid 2.454878 S.E. of regression 0.495467
R-squared 0.706575 Adjusted R-squared 0.677233
F(1, 10) 24.08028 P-value(F) 0.000617
Log-likelihood -7.506284 Akaike criterion 19.01257
Schwarz criterion 19.98238 Hannan-Quinn 18.65351
rho 0.519235 Durbin-Watson 0.745625
? series y = $yhat
Generated series y (ID 4)
? series y0 = v1 - y
Generated series y0 (ID 5)
? adf 1 y0
Augmented Dickey-Fuller test for y0
including one lag of (1-L)y0
sample size 10
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: -0.156
estimated value of (a - 1): -0.72329
test statistic: tau_c(1) = -2.48974
asymptotic p-value 0.1179
with constant and trend
model: (1-L)y = b0 + b1*t + (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: -0.494
estimated value of (a - 1): -0.675761
test statistic: tau_ct(1) = -2.74247
asymptotic p-value 0.2193
What is making the different on the t value and p value? The ols have no problem
The second problem is the save tab on the .show save the $uhat scatterplot against time and not
saving the $uhat from the scatterplot from v1 v2. They are quite different and adf apply
on both give different output
adf on $uhat scatterplot against time
? adf 1 y0
Augmented Dickey-Fuller test for y0
including one lag of (1-L)y0
sample size 10
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: -0.156
estimated value of (a - 1): -0.72329
test statistic: tau_c(1) = -2.48974
asymptotic p-value 0.1179
with constant and trend
model: (1-L)y = b0 + b1*t + (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: -0.494
estimated value of (a - 1): -0.675761
test statistic: tau_ct(1) = -2.74247
asymptotic p-value 0.2193
adf on $uhat scatterplot
? adf 1 y
Augmented Dickey-Fuller test for y
including one lag of (1-L)y
sample size 10
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: -0.167
estimated value of (a - 1): -0.169909
test statistic: tau_c(1) = -1.41724
asymptotic p-value 0.5755
with constant and trend
model: (1-L)y = b0 + b1*t + (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: -0.461
estimated value of (a - 1): -0.719062
test statistic: tau_ct(1) = -2.2661
asymptotic p-value 0.4521
Using series m = v1 - $yhat gives the $uhat against time. Have to manually export the
data and sort the $uhat against v2 rather time
Is there a way to save the $uhat against v2? There is a graph tab against v2 but how to save the $uhat against v2?
clarodina
