Earticle

초록

영어

In practice, Financial Time Series have serious volatility cluster, that is large volatility tend to be concentrated in a certain period of time, and small volatility tend to be concentrated in another period of time. While GARCH models can well describe the dynamic changes of the volatility of financial time series, and capture the cluster and heteroscedasticity phenomena. At the beginning of this paper, the definitions and basic theories of GARCH(1,1) models are discussed. Secondly, show the heavy tail behavior of GARCH(1,1) process with α-stable residuals {}ttZε∈, (0,2]α∈ and {}ttZε∈ errors. In fact, both these processes have heavy-tailed properties, but generally the tail of GARCH(1,1) process is heavier than the tail of {}ttZε∈ errors. And then the modification of maximum likelihood function has been constructed as the theoretical basis of this study, make use of Holder inequality and Jensen's inequality to estimate parameters of GARCH(1,1) model with residuals having regularly varying distributions with index 0α>. Finally, the consistency and asymptotic normality of the estimates constructed are further proved.

목차

Abstract
 1. Introduction
 2. GARCH (1,1) Models
 3. The Nature of Heavy Tails
  3.1. The Nature of Heavy Tails of Stable Distributions
  3.2. The Nature of Heavy Tails of GARCH(1,1) Process
 4. The Proof of Parameters Estimation Theory
 5. Conclusions
 Acknowledgements
 References

키워드

저자

• Hailong Chen [ College of Computer Science and Technology, Harbin Engineering University, School of Computer Science and Technology, Harbin University of Science and Technology ]
• Chunli Liu [ School of Computer Science and Technology, Harbin University of Science and Technology ]

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Signal Processing, Image Processing and Pattern Recognition

• 간기

  격월간

• pISSN

  2005-4254

• 수록기간

  2008~2016

• 십진분류

  KDC 505 DDC 605