Detection Of Change-point In ARCH And GARCH Models

The change-point analysis in financial time series has been regarded as one of the core areas of research in statistics. Recently, numerous studies related to this problem have been appear. This paper studies the problem, of testing and estimation of change-point in Autoregressive conditional Heteroscadastic (ARCH)Models and General Autoregressive conditional Heteroscadastic(GARCH) Models and obtains several results as follows:In chapter 2, we consider the change point test problem for GARCH models. The limiting distribution of test statistic under null hypothesis is proved to be the function of a standard Brownian.Chapter 3 studies the problem of multiple change point test in ARCH Models. The limiting distribution of the test under null hypothesis is obtained. The number of change points can be estimated via the test procedure. We showed that the estimator is consistent.This paper also considers the mean change point estimation in Chapter 4. The estimator is showed to be consistent.A number of simulation examples and real data analysis have been done to support the validity of methods in this paper.