本文選題：經(jīng)驗似然 + 漸近正態(tài)�。� 參考：《中國礦業(yè)大學》2015年碩士論文

【摘要】：經(jīng)驗似然方法是由Owen提出的一種非參數(shù)統(tǒng)計推斷方法,具有良好的漸近性質(zhì),如何將這種方法用于部分線性ARCH誤差模型的統(tǒng)計推斷是一個熱點的問題.雖然文獻中利用最大似然估計的方法構造了經(jīng)驗似然統(tǒng)計量,但要求誤差項的四階矩有限,這個要求一般對金融時間序列過于苛刻.因此,本文利用最小絕對偏差(LAD)估計方法構造經(jīng)驗似然統(tǒng)計量,在誤差項是厚尾分布的情況下,分別推導出LAD估計量和經(jīng)驗似然比統(tǒng)計量的漸近性質(zhì).最后,本文進行了蒙特卡羅模擬,模擬出這兩種方法的置信區(qū)域的覆蓋率,根據(jù)模擬所得到的結果比較了這兩種方法的優(yōu)越性.具體做了以下幾個方面的工作:第一,對部分線性ARCH誤差模型,構造參數(shù)的目標函數(shù),然后求目標函數(shù)的最小值,得到LAD估計量;第二,根據(jù)鞅的中心極限定理和遍歷性定理,證明了LAD估計量的漸近正態(tài)性,并且給出了漸近正態(tài)置信區(qū)域;第三,在LAD估計的基礎上,構造了經(jīng)驗似然比統(tǒng)計量,然后了證明經(jīng)驗似然比統(tǒng)計量的漸近性質(zhì),并且給出了經(jīng)驗似然置信區(qū)域;第四,進行數(shù)據(jù)模擬,計算置信區(qū)域的覆蓋率,通過進行對比,得出經(jīng)驗似然方法具有更好的優(yōu)越性.
[Abstract]:Empirical likelihood method is a nonparametric statistical inference method proposed by Owen. It has good asymptotic property. How to apply this method to the statistical inference of partial linear ARCH error model is a hot issue. Although the empirical likelihood statistics are constructed by using the method of maximum likelihood estimation in the literature, the fourth order moment of the error term is limited, which is generally too harsh for the financial time series. In this paper, the empirical likelihood statistics are constructed by using the method of minimum absolute deviation (lad) estimation. The asymptotic properties of the LAD estimator and the empirical likelihood ratio statistic are derived under the condition that the error term is a thick-tailed distribution. Finally, Monte Carlo simulation is carried out to simulate the confidence region coverage of the two methods, and the advantages of the two methods are compared according to the simulation results. The main work is as follows: firstly, the objective function of parameter is constructed for partial linear ARCH error model, then the minimum value of objective function is obtained, and the LAD estimator is obtained. Secondly, according to the central limit theorem and ergodicity theorem of martingale, The asymptotic normality of LAD estimator is proved, and the asymptotic normal confidence region is given. Thirdly, on the basis of LAD estimation, empirical likelihood ratio statistics are constructed, and the asymptotic properties of empirical likelihood ratio statistics are proved. And the empirical likelihood confidence region is given. Fourth, the data simulation, the calculation of confidence region coverage, through comparison, it is concluded that empirical likelihood method has better advantages.
【學位授予單位】：中國礦業(yè)大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O212.1

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