H. L. ZHAO ET AL.
Copyright © 2013 SciRes. OJAppS
3
According the asymptotic null distribution discussed
in last section, the p-value with the observed
is approximately that is very close
to 0, leading to the assertion that there exists a change-
point during the 270 eruptions of the Old Faithful geyser
in October 1980.
we have
when and are chosen to be constant, .
Liu and Qian (2010) suggests to use and
. Such a choice clearly satisfies. Another popu-
lar choice is , ; see Perron and
Vogelsang (1992). In p ar ticu l ar, if for ,
and where is the greatest integer
less than or equal to x, by Corollary A.3.1 of
and
4. Acknowledgements
The research is partially funded by the Fundamental Re-
search Funds for the Central Universities (No. 2011-IV-
116).
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We now apply the modified empirical likelihood method
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Figure 1. Scatter plot of 270 eruptions of the Old Faithful
geyser in October 1980 in Yellowstone National Park USA.
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