  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.
