The Study Of Functional Central Limit Theorems For ARMA-GJR-GARCH And Several Kinds Of GARCH Processes

Empirical shows that many types of economic data variance depends on the condition of information and then swings of the past. Bollerslev(1986) putted forward the GARCH model. Their generalizations and expansions have been very successful in modeling time varying volatility. And time series model of asymptotic process has an important effect on the financial data statistical inference, Functional central limit theorem plays an important role on the gradual process of the research.For example, the FCLT is needed to derive the asymptotic structure of statistics applied in the theory of change point detection, or to determine the limit distribution of the Dickey-Fuller statistics used in unit-root testing in AR-GARCH processes.In this paper, we study the time series model of functional central limit theorem, ARMA-GJR-GARCH process, ABSGARCH process, augmented GARCH process putted forward by Duan (1997) and MS-GJR-GARCH process are the main study object. Under the hypothesis of second order moment exist, first of all to prove that stationary ARMA-GJR-GARCH process, augmented GARCH process and MS-GJR-GARCH process are L2-NED, and the FCLT hold for them. At the same time, authenticate APGARCH process, ABSGARCH process, and EGARCH process as example.