Abstract: This paper considers the
change point analysis for parameters when observations are from a heavy tailed
distribution (regularly varying tails). The presence of a change point is tested
and the asymptotic null distribution of test statistics is derived. Under the
alternative hypothesis, the asymptotic distribution of test statistics and the
consistency of change point estimators are studied. We derive the limiting
distribution of change point estimators under the locally alternative. We mostly
assume that the observations are in the domain of attraction of a stable
distribution with index This
paper extends some of existing results in the estimation of parameters of stable
distributions to change point setting.
Keywords and phrases: Brownian bridge, change point, heavy tailed observations, stable bridge, stable process.
