Research On Parameters Estimation Of Time Series Model Based On Stable Distribution

This paper discusses several probability performances and index evaluationof heavy-tailed stable distribution, which is an important part of the distributionhaving regularly varying. Firstly, the definitions and basic theories of the Alphastable distribution are discussed as the theoretical basis of this study. Secondly,analyze the four commonly used parameterizations to generate random series ofAlpha stable distribution. The implementation of Alpha stable distributionrandom variable simulation is the foundation of this research. This paper providesthe generation algorithm of Alpha stable distribution based on the standardparameterization.Then we build the maximum likelihood estimate of stable distribution andthe GARCH(1,1) model parameters assessment which have a stable remainderand regular change of remainder of index greater than0. Construct themodification of maximum likelihood function to estimate the parameters ofGARCH(1,1) process with the errors having regularly varying distribution.Research the regularly varying index which is less than the unit1of theGARCH(1,1) model, and put forward the methods of Alpha stable distributionrandom modeling and parameter evaluation.In order to achieve the expected targets, this paper solve the followingproblems: find the corresponding relationships between parameters of thedifferent parameterizations, and build the generation of stable random variablesbased on the standard parameterization; Found a new way, you can find aasymptotic distribution of the GARCH(1,1) model parameters assessment whichhave a stable remainder and regular change of remainder of index greater than1.