Q-stat in ARMA models

[paroster]

Hi,

As far as I can tell, the test for autocorrelation in the residuals (Q-stat) is not correct when an ARMA model is specfified in terms of lagged dependent variables such as

y c y(-1)

(The problem, the way I see it, is that no correction is made for the number of AR terms. Hence, you here get a test statistic and p-value for the first lag.)

If, on the other hand you write the model as if the error term has an ARMA structure, such as

y c AR(1)

it is done correctly. (That is, the test is not conducted for the first lag - you don't get a p-value.)

Would you agree with me?

[EViews Glenn]

We see the behavior you are reporting. We'll look into the issue.

[EViews Glenn]

Sorry for the extended delay in answering this one. It generally doesn't take us this long to get something fixed but we wanted to make sure we got things right (or as right as possible).

We have modified EViews so that the Q-stat for AR models specified by list using lagged dependent regressors uses a d.f. that adjusts for the lagged dependent regressors. The tricky part in all of this is that Ljung-Box statistic is strictly valid in a very narrow range of specifications and we wanted to be more explicit about this narrow range. Accordingly, in a variety of settings, we have added messages to the output that warn that the asymptotic p-values may not be valid. We feel that this provides additional guidance in the use of these statistics.

I have checked the fixes into the EViews code base and they will appear in the next update (post 6/19/2013).

Note, that our messaging is generally conservative, as in, there are known models for which the p-values are valid but whose form makes it difficult for us to detect this fact. For example,

log(y) c log(y(-1))
log(y) c @lag(y, 2)

are specifications which are valid but will generate warning messages.

Lastly, I note that there are generalized versions of the Box-Pierce (Ljung-Box) statistics which are more generally valid and that that we might consider for inclusion in future versions of EViews. However, given the more general applicability of the existing serial correlation LM test statistics, it is not clear to us if there is demand for this style of portmanteu statistic. If anyone has opinions on this topic we welcome your comments and input.