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).

REFERENCES

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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

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