Change point detection in autoregressive models with no moment assumptions
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Date
2016
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Abstract
In this paper we consider the problem of detecting a change in the parameters
of an autoregressive process, where the moments of the innovation process
do not necessarily exist. An empirical likelihood ratio test for the existence
of a change point is proposed and its asymptotic properties are studied. In
contrast to other work on change point tests using empirical likelihood, we do
not assume knowledge of the location of the change point. In particular, we
prove that the maximizer of the empirical likelihood is a consistent estimator
for the parameters of the autoregressive model in the case of no change point
and derive the limiting distribution of the corresponding test statistic under
the null hypothesis. We also establish consistency of the new test. A nice
feature of the method consists in the fact that the resulting test is asymptotically
distribution free and does not require an estimate of the long run
variance. The asymptotic properties of the test are investigated by means of
a small simulation study, which demonstrates good finite sample properties of
the proposed method.
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Keywords
empirical likelihood, autoregressive processes, infinite variance, change point analysis