Automatic Lag Selection in COINTREG

[cgreene]

I apologize in advance, this is a long question.

I have been checking whether I can reproduce by hand the results for Eviews command Cointreg for DOLS estimation. For manual lead-lag structure I can do so. But I could use some hints about how Eviews uses the AIC or SIC to automatically select the dynamics. There are a lot of possibilities. Suppose the initial model includes 3 leads and 3 lags of the differenced variables. Eviews can decide that the info criteria implies one lead and two lags. But I am not sure how it gets there, because Eviews seems to change the sample trimming depending upon the leads and lags retained. In my experience there can be more than one local minima to the aic if the sample is changed as more or fewer lags or leads are retained. So I am not sure of the procedure followed by Eviews.

To make this discussion simple, suppose we are concerned only with lag (not lead) structure, and suppose the data has 100 observations and we are minimizing the SIC with at most ten lags. If I was determining lags retained by hand then I would first fix the sample to include observations 11-100. Then suppose I find that aic is minimized for 5 lags over this sample 11-100. Then I would fix the sample to include observations 6-100, and check whether the SIC still rises if I drop another lag. If the SIC was minimized for fewer lags, then I would repeat the process of extending the sample.

I can't tell if Eviews does something complicated like the above, or if it changes sample trimming each time a lead or lag is dropped, which is simple but may yield different results than yielded by holding the sample constant while searching for a local minimum.

Next, to add the complications of leads and lags together, Suppose there are initially 3 leads and 3 lags. Does Eviews proceed this way: Check the (say) SIC for 2 leads and 3 lags, versus 3 leads and 2 lags. Then suppose the smaller SIC is for 3 leads and 2 lags. The next step would be to check the SIC for 2 leads and 2 lags versus 3 leads and 1 lag. Etc. Or does Eviews proceed this way?: Calculate the SIC for all convolutions of 3, 2, 1, 0 leads with 3, 2, 1, 0 lag, then pick the min. One approach follows a gradient, while the other looks at all possibilities.

[EViews Glenn]

From memory...

The samples must all be the same. Take the full subset and then compute the criteria over all possible joint leads and lags.