Rule for maximum lag in ADF test
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Rule for maximum lag in ADF test
With regard to the maximum lag for the ADF unit root test, am I right in thinking that there is an additional rule in version 7 with T/3 replacing 12 in the Schwert rule- with the minimum of the two used?? If so, is there a reference for this?
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EViews Glenn
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Re: Rule for maximum lag in ADF test
I'm don't think that there is a specific reference (though I'm not certain about this...the most relevant reference is probably Ng and Perron---JASA 1996, Unit Root Tests in ARMA Models..., Section 3.1.2---who note the arbitrariness of the normalizing constants and exponent in the choice). I wasn't around the time-series group when this was implemented, but here's my interpretation of what's going on...
As you know, there are two Schwert "rules", the l4 and the l12. I use the term rule loosely since l4 and l12 are simply the values used by Schwert in his extensive simulations. The EViews rule appears to be a modified version of the Schwert l12 rule designed to reduce the lag length for very small sample sizes.
For those following along with the discussion, the Schwert l12 rule is: int(12(T/100)^(1/4)).
Note that from a practical point of view, the Schwert guidelines are problematic for very small sample sizes. For example with 5 observations, the Schwert rule specifies 5 lags, which clearly won't work. For 10 observations, strict application of the Schwert rule results in a choice of 6 lags, leaving only 4 observations for the unit root test. For 20 observations we have 8 lags and for 36 observations we have 9 lags. Clearly, some adjustment to the Schwert rule must be made for observations less than 6. The EViews adjustment extends this a bit by lowering the number of lags selected for observations less than 36 (three years of monthly data).
Now one might argue that one shouldn't be performing unit root tests with so few observations (and one really shouldn't) but software designers must account for the possibility that people might attempt to do so. Given the empirical sizes of the test statistics reported in Schwert for 25 observations (which are poor to begin with), there doesn't appear to be much harm in this adjustment. The adjustments may even help, though I wouldn't put money down on it.
Unfortunately, it appears to me that the documentation for EViews 6 did not describe the small-sample adjustment for ordinary unit root tests (it did describe the adjustment for panel variants of the tests). This has been corrected in the EViews 7 documentation, which is undoubtedly what you are responding to. Our apologies for any confusion.
As you know, there are two Schwert "rules", the l4 and the l12. I use the term rule loosely since l4 and l12 are simply the values used by Schwert in his extensive simulations. The EViews rule appears to be a modified version of the Schwert l12 rule designed to reduce the lag length for very small sample sizes.
For those following along with the discussion, the Schwert l12 rule is: int(12(T/100)^(1/4)).
Note that from a practical point of view, the Schwert guidelines are problematic for very small sample sizes. For example with 5 observations, the Schwert rule specifies 5 lags, which clearly won't work. For 10 observations, strict application of the Schwert rule results in a choice of 6 lags, leaving only 4 observations for the unit root test. For 20 observations we have 8 lags and for 36 observations we have 9 lags. Clearly, some adjustment to the Schwert rule must be made for observations less than 6. The EViews adjustment extends this a bit by lowering the number of lags selected for observations less than 36 (three years of monthly data).
Now one might argue that one shouldn't be performing unit root tests with so few observations (and one really shouldn't) but software designers must account for the possibility that people might attempt to do so. Given the empirical sizes of the test statistics reported in Schwert for 25 observations (which are poor to begin with), there doesn't appear to be much harm in this adjustment. The adjustments may even help, though I wouldn't put money down on it.
Unfortunately, it appears to me that the documentation for EViews 6 did not describe the small-sample adjustment for ordinary unit root tests (it did describe the adjustment for panel variants of the tests). This has been corrected in the EViews 7 documentation, which is undoubtedly what you are responding to. Our apologies for any confusion.
Re: Rule for maximum lag in ADF test
Many thanks for the full and prompt response- much appreciated.
Re: Rule for maximum lag in ADF test
Could someone please help me out with methods of determining the lag length of an ADF testing equation?
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