[Gretl-users] Cointegration Engle-Granger ?

[Allin Cottrell]

On Mon, 24 Jul 2006, john w wrote:

> Thnx Sven and Allin,
> Now I have another question related to EG cointegration in gretl.
> How do I know which is the optimal lag order in EG coint test?

Thanks for drawing attention to this test, which needed a bit 
more work!

First of all, mea culpa, I now believe there was an error in the 
selection of the p-value for the "tau" statistic in the 
Engle-Granger test, at least in some cases.

I think I misinterpreted the criterion for selecting between 
MacKinnon's tau_nc (no constant), tau_c (with constant), etc. 
I was using tau_nc for Engle-Granger, on the grounds that 
there's no constant in the (A)DF test for the residuals from the 
cointegrating regression (which of course have mean zero by 
construction).  But I now think, from re-reading MacKinnon 
(1996), that the relevant factor here is not the setup of the DF 
regression for the residuals, but whether or not the 
cointegrating regression itself includes a constant.  (If any 
time-series guru out there can confirm my new interpretation, 
I'd be grateful!)

Anyway, I've "corrected" the p-value-finding code on the 
assumption that my new interpretation is correct.  We now use 
tau_c if there's a constant in the cointegrating regression (the 
default), or tau_nc if the constant in that regression has been 
suppressed via the "--nc" flag to the "coint" command.

A few other things:

(1) In response to John W., you can now set a "maximum lag", 
rather than a specific lag, and have gretl test down from that 
maximum.  This works exactly as per the adf command (see the 
help entry for adf).  In command-line mode, as with adf, you 
make the "order" parameter negative to invoke this option; in 
GUI mode, you check the box "Test down from maximum lag order".

(2) If you reckon you already know enough about the stationarity 
properties of the individual variables involved, you can skip 
the initial per-variable (A)DF tests with the option flag 
"--skip-df" (or by checking "Skip initial DF tests" in the GUI).

(3) In case you want to base something on the AIC value, this is 
now shown for the cointegrating regression.

(4) The printouts for both the ADF test and the Engle-Granger 
test have been adjusted to make more explicit the distribution 
to which the given p-value pertains.  Instead of just saying "t 
statistic" we now say, for example, "tau_c(3) statistic", 
meaning that this is tau_c as set out by MacKinnon, and that it 
involves 3 (potentially) cointegrated variables.  (If anyone 
finds this opaque and has a suggestion for making it clearer, 
I'll listen.)

This is all in current CVS; a new Windows snapshot will follow 
shortly.

Allin.