Two ARCH Models and Their Limitations as Diffusion Processes  

作　　者：杨海波 叶俊 

出　　处：《Tsinghua Science and Technology》2002年第3期223-227,共5页清华大学学报（自然科学版（英文版）

基　　金：Supported by the National Natural Science Foundationof China(No.79970 12 0 )

摘　　要：Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Y k and σ 2 k denote the log returns and the volatility. When the time interval h goes to zero, (Y k,σ 2 k), as a discrete time Markov chain system, weakly converges to a continuous time diffusion process. The continuous time approximation of the ASDARCH model is done using two different methods. With some transformation, these two results are equivalent to high frequency data. The continuous time approximation of the APARCH model is obtained by a different procedure.Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Y k and σ 2 k denote the log returns and the volatility. When the time interval h goes to zero, (Y k,σ 2 k), as a discrete time Markov chain system, weakly converges to a continuous time diffusion process. The continuous time approximation of the ASDARCH model is done using two different methods. With some transformation, these two results are equivalent to high frequency data. The continuous time approximation of the APARCH model is obtained by a different procedure.

关 键 词：ASDARCH APARCH diffusion processes 

分 类 号：O211.6[理学—概率论与数理统计]