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dc.description.abstractGARCH(1, 1) 모형에 관한 기존의 많은 연구는 독립동등분포(i.i.d) 조건을 가정한다. 이는 이론적인 연구를 함에 있어 많은 편의를 제공하지만, 실제 데이터 분석 등의 실용적인 활용에서는 i.i.d 조건을 만족하지 않는 경우를 종종 찾아볼 수 있다. 이러한 필요성에 의해 이 논문에서는 i.i.d 조건을 mixing을 더한 strictly stationary 조건으로 완화하여, GARCH(1, 1) 모형을 확장한 augmented GARCH(1, 1) 모형들에 대하여 연구하였다. 한편 Nonstationary augmented GARCH(1, 1) 모형의 변동성은 시간이 지남에 따라 발산하는 특징을 갖는다. Nonstationary augmented GARCH(1, 1) 모형을 4가지 케이스로 나누고, 각 케이스의 변동성 대하여 적절히 변형을 하면, 시간이 지남에 따라 각 케이스의 변형된 변동성은 어떠한 극한분포로 수렴한다. 이를 증명하고, 시뮬레이션을 통해 확인한다.;We consider the augmented semi-strong GARCH (1, 1) model and prove the asymptotic behavior of the process when it is nonstationary. Augmented GARCH(1, 1) process includes many popular GARCH-type models such as TGARCH(1, 1), GJR-GARCH(1, 1), and EGARCH(1, 1). In many previous studies of the GARCH model, independent and identically distributed (i.i.d) innovations were assumed. The i.i.d assumption provides a great convenience in carrying out theoretical research, however, it often fails to meet the i.i.d assumption in real financial markets. Therefore, in this paper, the i.i.d assumption is weakened to strictly stationary condition and mixing assumption. In this paper, nonstationary GARCH (1, 1) type model is divided into four possible cases and the volatility of each case is properly transformed. It is shown that the transformed volatility converges into some limiting distribution for each case. Proofs and simulations are provided.-
dc.description.tableofcontentsI. Introduction 1 II. Model 5 III. Preliminaries and Assumptions 7 A. Stationarity 7 B. Birkhoff Ergodic Theorem 7 C. Mixing 8 D. Functional Central Limit Theorem 10 E. Assumptions 12 IV. Results 13 A. Theorem 4.1 13 B. Theorem 4.2 14 C. Theorem 4.3 14 D. Theorem 4.4 14 V. Proofs 15 A. Proof of Theorem 4.1 16 B. Proof of Theorem 4.2 18 C. Proof of Theorem 4.3 21 D. Proof of Theorem 4.4 25 VI. Simulated Study 26 A. Real Data Analysis 26 B. Simulations 28 Bibliography 31 Abstract(in Korean) 33-
dc.format.extent996982 bytes-
dc.publisher이화여자대학교 대학원-
dc.titleAsymptotic Behavior of Volatility in Nonstaionary Augmented GARCH(1, 1) Model with Stationary Mixing Errors-
dc.typeMaster's Thesis-
dc.creator.othernameKim, Jooyoung-
dc.format.pageiv, 33 p.-
dc.identifier.major대학원 통계학과- 8-
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