【摘要】：對于變點(diǎn)問題的研究最早是被應(yīng)用到工業(yè)質(zhì)量控制領(lǐng)域當(dāng)中,目前它不僅是在工業(yè)質(zhì)量控制領(lǐng)域里有大量的應(yīng)用,在經(jīng)濟(jì),金融,醫(yī)學(xué),計(jì)算機(jī),網(wǎng)絡(luò)安全,信號跟蹤等領(lǐng)域里也有很重要的應(yīng)用.近些年來,由于持久性變點(diǎn)問題在實(shí)際生活中有重要的應(yīng)用,因此對它的研究得到了經(jīng)濟(jì)學(xué)家的廣泛關(guān)注.但是許多與金融有關(guān)的數(shù)據(jù)都具有尖峰厚尾的特點(diǎn),因此對重尾序列持久性變點(diǎn)的研究顯得尤為重要.本文給出了兩種重尾持久性變點(diǎn)的檢驗(yàn)方法.第一種是在原假設(shè)為I(1),備擇假設(shè)為I(0)-I(1)下利用比率統(tǒng)計(jì)量來檢驗(yàn)變點(diǎn),第二種方法是在原假設(shè)為I(0),備擇假設(shè)為I(0)-I(1)下利用Wild bootstrap抽樣方法來對變點(diǎn)進(jìn)行檢驗(yàn).通過數(shù)值模擬得到了各自的經(jīng)驗(yàn)水平值和經(jīng)驗(yàn)勢函數(shù)值,發(fā)現(xiàn)這兩種方法對解決該問題都是有效的.論文主要由五部分組成.第一章是引言.本章主要對變點(diǎn)問題進(jìn)行了描述,并簡單介紹了已有的一些變點(diǎn)檢驗(yàn)的方法:極大似然法,最小二乘法,累積和法,經(jīng)驗(yàn)分位數(shù)法.第二章是理論基礎(chǔ)知識.本章主要介紹了與本文有關(guān)的一些背景知識.第三章是重尾持久性變點(diǎn)的比率檢驗(yàn).本章主要研究了原假設(shè)是I(l),備擇假設(shè)為I(0)-I(1)的殘差比率檢驗(yàn),并給出了它在原假設(shè)下的漸近分布和備擇假設(shè)下的收斂速度.通過數(shù)值模擬得到了此方法下的經(jīng)驗(yàn)水平值和經(jīng)驗(yàn)勢函數(shù)值.第四章是基于Wild bootstrap的重尾持久性變點(diǎn)檢驗(yàn).本章主要主要研究了原假設(shè)為I(0),備擇假設(shè)為I(0)-I(1)的殘差比率檢驗(yàn),并給出了它在原假設(shè)下的漸近分布.然后利用Wild bootstrap算法對其進(jìn)行抽樣,發(fā)現(xiàn)它們的漸近分布是一致的,通過數(shù)值模擬.得到了此方法下的經(jīng)驗(yàn)勢函數(shù)值.第五章是總結(jié).這一章對本文的主要內(nèi)容進(jìn)行了總結(jié).
[Abstract]:The study of the change point problem was first applied to the field of industrial quality control. At present, it not only has a large number of applications in the field of industrial quality control, but also in economics, finance, medicine, computer, network security. There are also important applications in areas such as signal tracking. In recent years, due to the important application of persistent change point problem in real life, its research has been widely concerned by economists. However, many data related to finance have the characteristics of peak and thick tail, so it is very important to study the persistent change point of heavy-tailed sequence. In this paper, two testing methods for persistent change points with heavy tail are given. The first method is to test the change point by using ratio statistics under the original hypothesis I (1) and the alternative assumption I (0) -I (1). The second method is to test the change point by using Wild bootstrap sampling method under the original assumption of I (0) and the alternative assumption of I (0) -I (1). The numerical simulation results show that both the empirical level and the empirical potential function are effective to solve the problem. The paper consists of five parts. The first chapter is the introduction. In this chapter, we mainly describe the problem of change points, and briefly introduce some existing methods of change point test: maximum likelihood method, least square method, cumulative sum method and empirical quantile method. The second chapter is the basic knowledge of theory. This chapter mainly introduces some background knowledge related to this paper. The third chapter is the ratio test of heavy-tailed persistent change points. In this chapter, we mainly study the residual ratio test of the I (l), alternative hypothesis I (0) -I (1), and give its asymptotic distribution under the original hypothesis and the convergence rate under the alternative hypothesis. The empirical level value and empirical potential function value are obtained by numerical simulation. Chapter 4 is the heavy-tailed persistence change point test based on Wild bootstrap. In this chapter, we study the residual ratio test of I (0) and I (0) I (1), and give its asymptotic distribution under the original hypothesis. Then the Wild bootstrap algorithm is used to sample them and it is found that their asymptotic distributions are consistent. The value of empirical potential function in this method is obtained. The fifth chapter is a summary. This chapter summarizes the main contents of this paper.
【學(xué)位授予單位】：山西大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1;F840

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本文編號：2207639