本文選題：重尾過程 + 協(xié)整過程�。� 參考：《山西大學(xué)》2016年碩士論文

【摘要】：協(xié)整過程是一種特殊的向量單位根過程,協(xié)整關(guān)系反應(yīng)變量之間存在著長期穩(wěn)定的均衡關(guān)系,在實際經(jīng)濟問題中,金融經(jīng)濟數(shù)據(jù)往往具有尖峰重尾的統(tǒng)計特點,難以用高斯分布去擬合,于是近年來重尾序列成為統(tǒng)計學(xué)及相關(guān)領(lǐng)域的一個研究熱點。重尾過程協(xié)整檢驗統(tǒng)計量的漸近分布中含有不可估計的重尾指數(shù)α,本文針對這個問題,在不估計重尾指數(shù)α的情況下,運用bootstrap抽樣和block bootstrap抽樣兩種算法,得出檢驗重尾過程協(xié)整關(guān)系的臨界值,證明在兩種抽樣算法下檢驗統(tǒng)計量的收斂性,并進(jìn)行實驗?zāi)M說明這兩種抽樣算法的有效性。本文共分為六章:第一章,前言,簡要介紹了協(xié)整過程及重尾過程的研究背景。第二章,預(yù)備知識,主要介紹了協(xié)整過程和重尾分布及其相關(guān)知識。第三章,介紹了重尾協(xié)整過程的bootstrap抽樣算法,證明了該算法的合理性并進(jìn)行Monte Carlo模擬說明該方法的有效性。第四章,介紹重尾協(xié)整過程的block bootstrap抽樣算法,進(jìn)行證明說明該算法的合理性,最后運用Monte Carlo模擬說明該方法的有效性,第五章,進(jìn)行實證分析,運用兩種抽樣算法對我國股票指數(shù)與經(jīng)濟增長進(jìn)行協(xié)整關(guān)系的檢驗。第六章,總結(jié)與展望,總結(jié)本文主要內(nèi)容,提出本文中兩種算法的不足之處,以及日后需要改進(jìn)的地方。
[Abstract]:The cointegration process is a special vector unit root process. There is a long-term stable equilibrium relationship between the cointegration response variables. In the actual economic problems, the financial economic data often have the statistical characteristics of sharp peak and heavy tail. It is difficult to fit with Gao Si distribution, so heavy-tailed sequence has become a hotspot in statistics and related fields in recent years. The asymptotic distribution of cointegration test statistics for heavy-tailed processes contains an inestimable heavy-tailed exponent 偽. In this paper, two algorithms, bootstrap sampling and block bootstrap sampling, are used to solve this problem without estimating the heavy-tailed exponent 偽. The critical value of cointegration relation of heavy-tailed process is obtained, and the convergence of the test statistics is proved under two sampling algorithms, and the validity of the two sampling algorithms is illustrated by experimental simulation. This paper is divided into six chapters: the first chapter, preface, briefly introduces the cointegration process and heavy-tailed process research background. The second chapter, preparatory knowledge, mainly introduces the cointegration process, heavy-tailed distribution and related knowledge. In chapter 3, the bootstrap sampling algorithm for heavy-tailed cointegration process is introduced, the rationality of the algorithm is proved and the validity of the method is illustrated by Monte Carlo simulation. In chapter 4, the block bootstrap sampling algorithm of heavy-tailed cointegration process is introduced, and the rationality of the algorithm is proved. Finally, the validity of the method is illustrated by Monte Carlo simulation. In chapter 5, the empirical analysis is carried out. Two sampling algorithms are used to test the cointegration relationship between stock index and economic growth in China. The sixth chapter summarizes and prospects the main contents of this paper and puts forward the shortcomings of the two algorithms in this paper as well as the future needs to be improved.
【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】：2016
【分類號】：O212;F224

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本文編號：1953768