Re: [Gretl-users] Cointegration Engle-Granger ?

On Mon, 24 Jul 2006, john w wrote: 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.