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On the stationarity of threshold garch(p,q) model with no continuity assumption

Title
On the stationarity of threshold garch(p,q) model with no continuity assumption
Authors
안선용
Issue Date
2003
Department/Major
대학원 통계학과
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
There are sufficient conditions for the stationarity and ergodicity of various Threshold AR and Threshold ARMA models. Especially, Ling(1999) showed the sufficient condition for the stationarity and ergodicity of general TARMA(p,q) model under Feller continuity. This paper provides the condition for the stationarity and ergodicity of a threshold GARCH(p,q) model and constructs a test function which leads to the results, using Tweedie's criteria. To ensure the existence of a finite positive invariant measure, besides requiring the existence of an appropriate test function, we need "uniform countable additivity" condition. First, this paper provide the condition and we show that threshold GARCH(p,q) model satisfies the "uniform countable additivity" condition. And then we construct a special test function which leads to stationarity and finiteness of the moments of a threshold GARCH(p,q) model.;다양한 Threshold AR 와 Threshold ARMA 모델들의 stationarity와 ergodicity를 위한 충분한 조건들이 많다. 특별히, Ling(1999)은 Feller continuity 저건아래에서 일반적인 TRAMA(p,q) 모델의 stationarity와 ergodicity를 위한 조건을 제시하고, Tweedie's criteria를 사용하는 결과들을 초래하는 검정함수(test function)를 만들고자 한다. Finite positive invariant measure의 존재성을 보장하기 위하여, 게다가 적절한 검정함수(test function)의 존재성을 위하여 우리는 uniform countable additivity 조건이 필요하다. 우선, 본 논문에서는 그 uniform countable additivity조건을 제공하고 threshold GARCH(p,q)모델이 그 조건을 만족하는지를 보인다. 다음으로, 우리는 Thershold GARCH(p,q) 모델의 moments의 stationarity와 finiteness를 이끄는 특별한 검정함수(test function)를 만든다.
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