Re: [Gretl-users] LW estimator and the GPH test
Hi,
just wanted to say, although normally I'm not a very big fan of
discussing general econometrics questions unrelated to gretl on this
list, I found the quality of Javier's post impressive. Clear, concise,
and even comes with a list of references, wow!
¡Vaya campeón!
cheers,
sven
Am 10.08.2010 16:55, schrieb Javier García:
Hi, everybody;
LW and GPH estimators are consistent for d=<1 and asymptotically
normal for d<0.75 (see Velasco, 1999a, 1999b, Phillips and Shimotsu,
2004 and Phillips, 2007), but LW is more efficient. Besides, the
asymptotic variance depends on the bandwidth (and, normally, the
bigger the sample size the bigger the bandwidth). If you want to test
the hypothesis of unit root you should apply the test on the first
differences of the series and test if the memory parameter is equal
zero. If you don't reject that hypothesis, the series seems to have a
unit root. To avoid differenciation, there are other posibilities:
tapering (Velasco, 1999a, 1999b), ELW of Shimotsu and Phillips
(2005), non-local estimators (Abadir et Al., 2007), etc.
Cheers Javi
References:
Velasco, C., 1999a. Gaussian semiparametric estimation of
non-stationary time series. J. Time Ser. Anal. 20, 87-127. Velasco,
C., 1999b. ‘Non-Stationary Log-Periodogram Regression
<http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VC0-3WS6R33...,
Journal of Econometrics, 91, 325-371
Phillips, P.C.B., Shimotsu, K. (2004). Local Whittle estimation in
nonstationary and unit root cases. Ann. Stat. 32, 656-692.
PHILLIPS, P.C.B. (2007): Unit root log periodogram regression.
Journal of Econometrics 138(1), 104-124.
ABADIR, K.M., DISTASO, W. and GIRAITIS, L. (2007):
Nonstationary-extended local Whittle estimation. Journal of
Econometrics 141, 1353-1384.
SHIMOTSU, K. and PHILLIPS, P.C.B (2005): Exact local Whittle
estimation of fractional integration. The Annals of Statistics 33(4),
1890-1933.
1.
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