統計数学セミナー
Seminar on Probability and Statistics |
Home : Archive [ 2003 to 04 ] [ 2004 to 05 ] [ 2005 to 06 ] [ 2006 to 07 ] [ 2007 to 08 ] [ 2008 to 09 ] [ 2009 to 10 ] [ 2010 to 11 ] [ 2011 to 12 ] [ 2012 to 13 ] [ 2013 to 14 ] [ 2014 to 15 ] |
Previous Seminar : Next Seminar |
Seminar on Probability and Statistics Wednesday January 31 2007 Tokyo 128 4:20-5:30 pm
A Sequential Unit Root Test
西山 慶彦 / NISHIYAMA, Yoshihiko 京都大学経済研究所 / Institute of Economic Research Abstract It is well known that conventional unit root tests such as
Dickey=Fuller and
its variants do not have good power properties when sample size is not
large. Lai and Siegmund (1983, AS) proved that OLS estimator of the
AR(1)
coefficient is asymptotically normally distributed in a sequential
framework
even if the time series has a unit root unlike the OLS estimator under a
standard sampling scheme. We pursue this direction to propose a unit
root test under a sequential sampling. The proposed test uses not only
the
OLS estimator of the AR(1) coefficient, which is asymptotically normal,
but
also the stopping time to construct the critical region, anticipating a
better power
property. We obtain analytic expressions of the joint distribution of
the two
statistics as well as its marginals under the null. We also consider
the distribution
of the statistics under local alternatives. The properties of the
stopping time,
to the best of our knowledge, have not been studied in the unit root
literature.
We calculate its expectation and variance.
|
Previous Seminar : Next Seminar | Seminar on Probability and Statistics |