Re: [Gretl-users] displayed Engle-Granger model missing terms
Lets take some time series variables in levels. Say Ramanathan data2-3 in gretl samples,
Unemployment, Inflation and wages. Lets say we choose infl and wggr. Proceed to the
following menu:
Model -> Time Series -> Cointegration test -> Engle-Granger
Cointegration menu:
Variables to test: infl, wggr // in that order
lag order 5
Test down from maximum lag order: check
Skip initial DF tests: check
test with constant // in dropdown
This produces a result with two sections... Step 1: cointegrating regression and Step 2:
testing for a unit root in uhat.
I don't have issues with Step 1, since I see the const term I asked to be included
(misspecification issues aside, however this is pre-OLS residuals test):
Step 1: cointegrating regression
Cointegrating regression -
OLS, using observations 1959-1995 (T = 37)
Dependent variable: infl
coefficient std. error t-ratio p-value
--------------------------------------------------------
const −0.402450 0.967337 −0.4160 0.6799
wggr 1.09502 0.193428 5.661 2.16e-06 ***
Step 2 is where i have concerns since I was expecting a b0 term in
model: (1-L)y = (a-1)*y(-1) + ... + e
I explicitly chose to include a constant, therefore I was expecting something like:
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
Step 2: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including 6 lags of (1-L)uhat
(max was 8, criterion modified AIC)
sample size 30
unit-root null hypothesis: a = 1
model: (1-L)y = (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.052
lagged differences: F(6, 23) = 1.652 [0.1782]
estimated value of (a - 1): -0.476897
test statistic: tau_c(2) = -1.62764
asymptotic p-value 0.7108
It seems to be dataset independent, I tested it on three separate ones. In fact, I am not
claiming that calculations in Step 2 are off. My only concern is that I'm not seeing
the model I expected since I asked the software to include the constant term.
On Tuesday, February 16, 2016 8:35 PM, Allin Cottrell <cottrell(a)wfu.edu> wrote:
On Tue, 16 Feb 2016, Salman Khan wrote:
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.
Please tell us exactly what you are doing (which menu, which
options). In the final step of an Engle-Granger test based on a OLS
regression residual there had better not be any constant, etc.,
unless the OLS procedure is broken.
Allin Cottrell