The Study Of Variance Estimation For Linear Model With FBM

The analysis of linear model with fractional brownian motion is a very important study in probability and statistics field.The parameter estimation,especially the vari-ance estimation for the model,has wide application in econometrics and finance.This article is mainly about the variance estimation in linear model with fractional brownian motion.The first section of chapter 2 is the background of maximum likelihood esti-mator and its properties from the work of Y.Z.Hu;the latter two sections is based on existed work,computing the first four moments and cumulants of the estimator,then we claim the Edgeworth expansion series for the variance estimation.In first section of chapter 3,we introduce the financial price volatility model with stochastic noise and estimator of variance from the work of L.Zhang,etc.The latter three sections we obtain the moment and cumulant approximation,also the large deviation based on the estimaor by L.Zhang,etc.In addition,we also get some properties of the distribution function for some estimator.