The Statistical Analysis For Multiple Change Points In GARCH Models

The generalized autoregressive conditional heteroskedasticity processes(GARCH)contain variance lagged term, and GARCH models can describe the dynamic characteristics of the conditional variance more effectively. Thus, GARCH models have been widely used in the financial field. However, the phenomena of parameters’ change-points in GARCH models has effects on its statistical property in the reality. So it is necessary to study the parameters’ multiple-change-points problem in GARCH models. This problem is studied in this thesis. The main results of this paper are briefly listed as follows:First, the parameters’ multiple-change-points problem of autoregressive moving average models(ARMA) is considered. To study this problem, the Sup F test statistic is constructed, and the limit distribution under null hypothesis is derived. By using Monte Carlo method, the quantile and the empirical distribution diagram of this test statistic are obtained. In order to verify the feasibility of the Sup F statistic, the efficiency based on the simulated result is analyzed.Second, the parameters’ multiple-change-points problem in GARCH(1,1) models is studied. Since GARCH(1,1) models contain variance lagged term, the GARCH(1,1) models are transformed into ARMA(1,1) models. In other words, this problem is transformed into the parameters’ multiple-change-points problem in ARMA(1,1) models. The Sup F test statistic is constructed, and the limit distribution under null hypothesis is derived. By using Monte Carlo method, the quantile and the empirical distribution diagram of this test statistic are also given. To verify the feasibility of the Sup F statistic, the corresponding efficiency based on the simulated result is illustrated.