Extrapolated Extreme Condition Quantile Estimation Based On Intermediate Order Quantile And Its Application

People often ignore things that rarely happen in daily life.However,once those happen,they will have a great impact on people's life,such as extreme rainfall,heavy financial losses,etc.These extreme events are usually affected by some covariates.Quantile regression provides a convenient and effective way to quantify the influence of covariates on different quantiles of the response distribution.However,due to the sparsity of the tail data,using quantile regression to estimate the extreme conditional quantile is usually unstable and will have large estimation errors.This thesis combines extreme value theory with quantile regression,and uses intermediate conditional quantile extrapolation to study the estimation of the extreme quantile level at the tail of the linear quantile regression model.Firstly,some conditional quantiles of intermediate level are estimated by quantile regression.In this thesis,the regression coefficients are divided into two cases: the same slopes and different ones.Secondly,a class of extreme value exponents are constructed by kernel function.Finally,using the second order condition of extreme value theory,the intermediate order quantile is extrapolated to the extreme tail to estimate the extreme condition quantile,and the corresponding asymptotic normality proof is given.In order to test the effectiveness of the proposed method,numerical simulation is carried out.The results show that the estimation of extreme conditional quantile is less affected by the number of intermediate quantiles,regardless of whether the slope of quantile regression model is equal or not.Therefore,the proposed method solves the problem of the number of intermediate quartiles to a certain extent,and reduces the high variance estimated by the model because of its different number.This thesis mainly studies the risk value Va R of the daily return sequence of Western oil stocks in the empirical part,and analyzes several factors that affect the Va R of risk value.It is concluded that the Va R of the daily return rate of Western oil stocks shows a positive change with the lag of Western oil stocks and Dow Jones industrial index by one day,and presents a negative change with the lag of Brent crude oil futures price by one day.