Distinguishing between random walks and changes in the mean 
Alexander Aue
Ph.D., Clemson University
Thursday, February 1, 2007
4:10 p.m.
C146 Clark
ABSTRACT
In this talk we discuss test procedures that detect structural breaks in underlying data sequences.
In particular, we wish to discriminate between different reasons for the breaks,
such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations
switching from stationarity to difference stationarity. Almost all procedures presently
available in the literature are simultaneously sensitive to all three types of alternatives.
The test statistics under consideration here are based on functionals of the partial sums
of observations. These CUSUMtype statistics have limit distributions if the mean remains
constant and the errors satisfy the central limit theorem, but tend to infinity in the case
any of the alternatives (1), (2) or (3) holds. On removing the effect of the shifting mean,
however, divergence of the test statistics will only occur under the random walk behavior,
which in turn enables statisticians to not only detect structural breaks but also to specify
their causes.
