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A Continuous-time Asymmetric Power GARCH(1,1) model driven by a Lévy process

Title
A Continuous-time Asymmetric Power GARCH(1,1) model driven by a Lévy process
Authors
송지혜
Issue Date
2011
Department/Major
대학원 통계학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
이외숙
Abstract
The autoregressive conditional heteroscedastic model (ARCH) and the classical generalized autoregressive conditional heteroscedastic model (GARCH) were introduced by Engle(1982) and Bollerslev(1986). The GARCH model explains the time varying volatility and heavy tail property, and many extension of classical GARCH model have been developed. One of these extension of classical GARCH model is the asymmetric power GARCH model (APARCH) introduced by Ding, Granger and Engle (1993). In this paper, we consider 'COAPGARCH'(Continuous-time Asymmetric Power GARCH) model, based on a single background driving Lévy process, which is an extension of the discrete-time APARCH process. We suggest a 'COAPGARCH' model and study stochastic differential equation ,stationarity and moments conditions.;Engle(1982) and Bollerslev(1986)에 의해 ARCH/GARCH 모형이 소개되었다. GARCH 모형은 시간에 따른 자료 변동성과 heavy tail 을 설명해 준다. 또한 classical GARCH의 확장 모형이 발전되어왔다. 이러한 확장된 모형 중 하나가 Ding, Granger and Engle (1993)에 의해 소개된 asymmetric power GARCH (APARCH) 모형이다. 이 논문에서는 이산 시간에서의 APARCH 모형을 Lévy process를 기반으로 연속시간에서의 APARCH 모형으로 확장하고자 한다. 즉, 'COAPGARCH' (Continuous-time Asymmetric Power GARCH) 모델을 제안하고자 한다. 그리고 이 모형에 대한 stochastic differential equation와 stationarity 그리고 moments conditions에 대해 연구한다.
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