Hello,
I have a toy time series dataset consisting of two variables. Running Engle-Granger tests,
I noticed that the displayed "model" in step 2 looks misspecifed. It could just
be an optical issue since the calculated values seem fine (haven't double check
against another package). Regardless of the option chosen in the dialog box (constant,
constant with trend, constant and quadratic), the resulting model in step 2 is listed as:
model: (1-L)y = (a-1)*y(-1) + ... + e
However, Step 1 seems to be fine wherein the regression table shows whether the constant,
trend and quadratic terms are selected or omitted.
Maybe I'm making an obvious error somewhere. Still trying to find my way around Gretl.
Thanks.
Linux Mint 17.3 64bit
gretl 1.9.14
/* test without constant */
Step 2: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including 5 lags of (1-L)uhat
(max was 8, criterion modified AIC)
sample size 498
unit-root null hypothesis: a = 1
// this seems fine model: (1-L)y = (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.001
lagged differences: F(5, 492) = 10.556 [0.0000]
estimated value of (a - 1): -0.0935336
test statistic: tau_nc(2) = -3.6509
asymptotic p-value 0.003718
/* test with constant */
Step 2: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including 5 lags of (1-L)uhat
(max was 8, criterion modified AIC)
sample size 498
unit-root null hypothesis: a = 1
// b0 term here missing?
model: (1-L)y = (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.001
lagged differences: F(5, 492) = 10.569 [0.0000]
estimated value of (a - 1): -0.0937828
test statistic: tau_c(2) = -3.64666
asymptotic p-value 0.02145
/* test with constant and trend */
Step 2: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including 5 lags of (1-L)uhat
(max was 8, criterion modified AIC)
sample size 498
unit-root null hypothesis: a = 1
// b0 and trend term here missing?
model: (1-L)y = (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.001
lagged differences: F(5, 492) = 10.013 [0.0000]
estimated value of (a - 1): -0.114083
test statistic: tau_ct(2) = -4.02716
asymptotic p-value 0.02529
/* test with constant and quadratic trend */
Step 2: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including 5 lags of (1-L)uhat
(max was 8, criterion modified AIC)
sample size 498
unit-root null hypothesis: a = 1
// terms missing here?
model: (1-L)y = (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.002
lagged differences: F(5, 492) = 8.788 [0.0000]
estimated value of (a - 1): -0.136323
test statistic: tau_ctt(2) = -4.47415
asymptotic p-value 0.02002