The basic DF test involves a regression of \delta y_t on y_{t-1}.
The ADF test then adds k lags of \delta y_t to this regression to
remove serial correlation from the disturbance.
If one considers the DF test as a regression of y_t on y_{t-1} then
one would need to also add the same number of additional lags to the
equation to remove the serial correlation. Thus in a sense the number
of additional lags required is the same regardless of which approach
one takes. I would tend to use the first always.
Best Regards
John
2008/12/4 Sven Schreiber <svetosch(a)gmx.net>:
Am 04.12.2008 21:28, Allin Cottrell schrieb:
> On Thu, 4 Dec 2008, Sven Schreiber wrote:
>
>> I just noticed that in the ADF test specification and output
>> it's not 100% obvious (at least to me) whether the lag order
>> refers to right-hand levels or differences. I would suggest that
>> at least in the output this should be clarified. (It could be in
>> the manual, I haven't checked right now, but in any case it
>> should be self-explanatory IMHO.)
>
> It's explicit in section 20.3 of the manual. The wording in the
> command help refers to "lags of the dependent variable", and this
> phrase appears under an equation which shows (1 - L)y_t as the
> dependent variable in the test regression, which in turn is
> prefaced by the statement, "In all cases the dependent variable is
> the first difference of the specified variable, y".
>
> So I'd say it's reasonably clear -- given, also, that surely
> that's what everyone would expect?
>
It's absolutely clear in the help and manual, no doubt. That lag orders
always refer to the dependent variable in unit-root contexts however is
_not_ a universal convention. Quite often the description starts with
levels and only after assuming unit roots differences are taken. In that
case the lag order of the differences are given as k-1 for example
(where k is the lag order of levels).
It's no big deal; if I really need to know I would look it up in the
help and I would find it. However, there is already a model description
line in the standard ADF test output exactly so that people don't always
have to read the manual. All I'm saying is that it might be useful to
change that line so that the lag order thing is clarified, too.
thanks,
sven
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