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   -> Volume 7, Issue 7


Preprint: Test for Homogeneity of Variance
 
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Brandon Whitcher (brandon@stat.washington.edu)
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PostPosted: Thu Jul 02, 1998 5:27 am    
Subject: Preprint: Test for Homogeneity of Variance
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#1 Preprint: Test for Homogeneity of Variance

A preprint is currently available on testing homogeneity of variance
in the presence of long-range dependence. It has been submitted for
publication.

Title: Testing for Homogeneity of Variance in Time Series: Long
Memory, Wavelets and the Nile River

Authors: B. Whitcher, S. D. Byers, P. Guttorp and D. B. Percival

Abstract:

We consider the problem of testing for homogeneity of variance in a
time series that has long memory structure. We demonstrate that a test
whose null hypothesis is designed to be white noise can in fact be
applied, on a scale by scale basis, to the discrete wavelet transform
of long memory processes. In particular, we show that evaluating a
normalized cumulative sum of squares test statistic using critical
levels appropriate for the null hypothesis of white noise yields
approximately the same null hypothesis rejection rates when applied to
the discrete wavelet transform of samples from a fractional difference
process. The point at which the test statistic, using the maximal
overlap discrete wavelet transform, achieves its maximum value can be
used to estimate the time of the unknown variance change. We apply our
proposed test statistic on a time series of Nile River yearly minimum
water levels covering the years 622 to 1284 AD. The test confirms an
inhomogeneity of variance at short scales and identifies the change
point around 720 AD, which coincides closely with the construction of
a new device in 715 AD for measuring Nile River water levels.

It is available via http://ftp.statsci.com/pub/longmem/lmwnr.ps

Brandon

Brandon Whitcher
University of Washington, Department of Statistics
Box 354322, Seattle, WA 98195-4322, USA (206) 685-3027
brandon@stat.washington.edu http://www.stat.washington.edu/brandon/
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