Quasi-likelihood Statistical Inference For GARCH,SV And Diffusion Models

In classical financial time series and functional financial time series modeling,volatility models GARCH,SV and diffusion process are mainstream m odels.What's more,GARCH and SV models have the same diffusion process as their 1 imits.In the statistical inference of these models-parameter estimation and hypothesis testing,the quasi likelihood method has been widely used,which is often due to the fact that the real likelihood function can not be obtained in reality.At the time of writing of this paper,there are a lot of research achievements on statistical inference methods of quasi-likelihood based on GARCH,SV and diffusion m odel.This paper combs and reviews these achievements and makes corresponding promotion.It is mainly promoted in the following two aspects:first,the limit distribution of general statistics under alternative hypothesis is derived from the limit distribution of quasilikelihood ratio of GARCH,SV and diffusion model under zero hypothesis,which provides theoretical support for some statistical application scenarios requiring alternative hypothesis distribution such as efficacy an alysis;Se condly,the qu asi-maximum li kelihood parameter estimation method of functional GARCH model is extended to functional multiplicative GARCH model,and the consistency of quasi-maximum likelihood parameter estimation is proved.