Estimator for the Heavy Tailed Index with the Stable Distribution
Hailong Chen, Zhang Yan, Fei Huang · International Journal of Signal Processing Image Processing and Pattern Recognition · 2017
Marginal distributions in the field of high frequency time series data of almost all type of heavy-tailed.It shows the importance of the study of heavy-tailed.Kesten's theorem combines Garch model parameters and stochastic equations to identify a property of a regular variation of GARCH model joint distributions.This paper has shown that finitedimensional joint distributions of GARCH model by Kesten are regularly varying distributions, and these distributions constitute heavy tailed distributions.We prove regular variation of the solution to the stochastic recurrent equation By Kesten's theorem, and the property of regular variation of finite joint distribution of the GARCH model has been proven, heavy tail index of ARCH(1) model distribution with stable residuals having a -stable distribution , 2 1 ~(1,0,0) S .At last the nature of the relevant index estimates and conclusions are given.