Mean Square Error Of Kernel-type Estimator And Its Applications For VaR Under P-Mixing Assumptions

The risk is one of the basic attributes of financial system and financial activ-ity, risk management play a very important role in the financial,economical and insurance area.The most important of risk management is risk measurement which directly relates to the usefulness of risk management.For what is risk, people can hardly strictly define or give a quantity for accurate depict risk,so appear vari-ous kinds of quantity depicts risk, such as:Standard Deviation, Absolute Deviation ,Value at Risk(VaR), Conditional Value at Risk(CVaR),Expected Shortfall(ES). Etc.VaR has been widely expanded by risk management with its special advan-tage.It is used to measure the biggest loss that financial property may suffered over a holding period.It is a generous character tool that is easily in practical and can synthesize to reflect the risk that financial property bears.Currently,VaR is main method take charge by financial supervision and risk management.It is also adopted by main bank in the world, non-bank organization financing institution, company and finance organization.The first question the risk management faces to is how to give an accurate es-timated of VaR.The earliest VaR estimates required assuming the distribution of return series and carried on an estimate of VaR under the premise.In fact, the form of financial return series is complication and change more,the return series is dif-ficult to be in conformity with the assumption condition under parameter mode. So use a parameter estimate method to easily produce model error.The last few years,many scholars start research on non-parameter estimate method to VaR. Non-parameter method is a free distribution returns series.It can flexibly deal with non-symmetric and "fat-tail" "peak" problem of return series.Therefore it has at- tracted widespread interest.This article studies VaR value of the non-parameter evaluation in the long-range sequence.The research model of VaR is Vh,λ= - Tn(λ),whereTn(λ)isλ-quantile estimator.The form is:Among them,X1, X2,..., Xnis a sample that comes from distributing func-tion F(x), X(i)is a sample i order of sequence.at the earliest stage,Tn(λ)was put forward by Parzen(1979),many scholars discussed some of its properties. Simon(1990)gave it's mean square error and a bandwidth selection method Un-der the independent variables.Wei Xianglan(2009)discuss the VaR kernel-type es-timation underα-mixing sequences,and to give the mean square error by using the Bahadur expression of Shanchao Yang(2006).This article discussρ—mixing se-quences under this estimation and its application.The key of applied problem is the choice of bandwidth selection.We apply the least of mean square estimate,Get the optimal bandwidth.And make use of the sequence ARMA model haveρ—mixture of the structure carry on numerical simulation By compared different estimation bias,we analysis the effect of our estimation model.Finally,the demonstration anal-ysis fuethmore show usefulness of our model.