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help for ^dfgls^                                 (STB-57: sts15; STB-58: sts15.1)
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Dickey-Fuller/Generalized Least Squares unit root test
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    ^dfgls^ varname  [^if^ exp] [^in^ range] [^,^ ^m^axlag^(^#^)^ ^not^rend ^ERS^]


^dfgls^ is for use with time-series data.  You must ^tsset^ your data before
using ^dfgls^; see help @tsset@.

varname may contain time-series operators; see help @varlist@.


Description
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^dfgls^ performs the Elliott-Rothenberg-Stock (ERS, 1996) efficient test for an
autoregressive unit root. This test is similar to an (augmented) Dickey-Fuller
"t" test, as performed by ^dfuller^ but has the best overall performance in
terms of small-sample size and power, dominating the ordinary Dickey-Fuller 
test. The ^dfgls^ test "has substantially improved power when an unknown mean 
or trend is present" (ERS, p.813). 

The test applies a GLS detrending (demeaning) step to the varname; 
the detrended (demeaned) series is then tested via the Dickey-Fuller 
regression. Demeaning is only performed if the ^notrend^ option is specified.
The maximum lag order for the test is by default calculated from the sample
size, using a rule provided by Schwert (1989) using c=12 and d=4 in his
terminology. The maximum lag order may also be provided with the ^maxlag^
option and may be zero. If the maximum lag order exceeds one, the test 
is performed for each lag, with the sample size held constant over lags 
at the maximum available sample. 

Approximate 5% and 10% critical values, by default, are calculated from the
response surface estimates of Table 1, Cheung and Lai (1995), which take both 
the sample size and the lag specification into account. Approximate 1% critical
values for the GLS detrended test are interpolated from ERS, Table 1 (p.825). 
Approximate 1% critical values for the GLS demeaned test are identical to 
those applicable to the no-constant, no-trend Dickey-Fuller test 
and are computed using the ^dfuller^ code. The ^ERS^ option specifies that
the ERS (and Dickey-Fuller) values are to be used for all levels of 
significance (eschewing the response surface estimates).

If the maximum lag order exceeds one, the optimal lag order is calculated
by the Ng-Perron (1995) sequential t test on the highest order lag coefficient,
stopping when that coefficient's p-value is less than 0.10. The lag minimizing 
the SC (BIC) criterion is printed with its minimized value. The lag minimizing
the Ng-Perron (2000) modified AIC, or MAIC, is also printed with its minimized
value. Ng and Perron have established that the MAIC may provide "huge size 
improvements" in the DFGLS context. The DF-GLS test statistic, seq-t optimal 
lag order, RMSE (calculated from sample size T) and values of the MAIC and SC 
for each lag are placed in the return array.


Options
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^maxlag(^#^)^ specifies the maximum lag order to be used in augmenting the 
Dickey-Fuller regression. If omitted, the maximum lag order is calculated
as described above.

^notrend^ indicates that GLS demeaning, rather than GLS detrending, is to
be performed.


Examples
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	. ^dfgls gnp^

	. ^dfgls gnp, maxlag(12) notrend^
	
	. ^dfgls gnp if tin(1973q1,1995q4)^


Authors
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Christopher F Baum, Boston College, USA
baum@@bc.edu

Richard Sperling, The Ohio State University, USA
rsperling@@boo.net

Also see
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    STB:  STB-57: sts15; STB-58: sts15.1
 Manual:  ^[R] dfuller^
On-line:  help for @dfuller@, @time@, @tsset@