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Uniform Ergodicity for Exponential Continuous-time GARCH Process

Title
Uniform Ergodicity for Exponential Continuous-time GARCH Process
Authors
이정은
Issue Date
2011
Department/Major
대학원 통계학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
이외숙
Abstract
The generalized autoregressive conditional heteroskadasticity model (GARCH) was proposed by Bollerslev(1986) explaining volatility and dependence in financial data. Nelson(1991) introduced the exponential GARCH model (EGARCH), which is the one of various GARCH models being able to explain asymmetry. The exponential continuous time GARCH model, called ECOGARCH, was introduced by Haug and Czado(2007). This model replaced the noise processes of discrete time EGARCH model by the increments of a Lévy process. In this paper, we give the condition for uniform ergodicity of ECOGARCH and prove it by using drift condition and the extended generator of the process.;재무 자료에서 변동성 등을 설명하는데 유용한 GARCH 모형은 Bollerslev(1986) 에 의해 소개되었다. 이후, 여러 GARCH 모형 중 Nelson(1991)이 소개한 exponential GARCH (EGARCH) 모형은 자료의 비대칭성을 잘 설명해주었다. Haug와 Czado(2007) 에 의해 제안된 exponential continuous-time GARCH 모형은 EGARCH 모형에서 이산시간의 noise process 를 Lévy process 로 대체하며 연속시간을 반영하였다. 이 논문에서는 ECOGARCH 모형의 uniform ergodicity 를 위한 조건을 제시하고, 증명을 위해 drift condition과 extended generator를 이용하였다.
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