本文選題：持久性變點 + 厚尾指數(shù)變點�。� 參考：《西安科技大學》2017年碩士論文

【摘要】：變點分析作為統(tǒng)計學領域的重要研究課題,一直以來都是國內外學者研究的熱點問題。近二十年來越來越多的理論證明,許多經(jīng)濟和金融數(shù)據(jù)展現(xiàn)持久性特征,且金融數(shù)據(jù)中出現(xiàn)的“尖峰厚尾”特性能夠被厚尾序列更好的刻畫。因此,對厚尾序列持久性變點的研究就顯得尤為重要。針對厚尾指數(shù)較小時,類方差比統(tǒng)計量檢驗的勢函數(shù)值偏小的現(xiàn)象,本文在第二章中提出了厚尾序列持久性變點截尾檢驗方法,通過對原始數(shù)據(jù)截尾處理,達到提高檢驗勢函數(shù)值效果。同時,還得到關于持久性變點位置的一致估計。經(jīng)過截尾處理之后類方差比統(tǒng)計量是穩(wěn)健的,即其極限分布是與厚尾指數(shù)無關,從而使得在厚尾指數(shù)較小的情況下也有良好的檢驗效果。數(shù)值模擬表明,在原假設下,截尾檢驗并沒有明顯優(yōu)勢;但在備則假設下能有效的提高檢驗勢函數(shù)值。第三章中研究了厚尾指數(shù)變點對持久性變點檢驗的影響。在原假設不存在持久性變點,但含有指數(shù)變點的情況下,厚尾指數(shù)由大變小即12時,則統(tǒng)計量以2/2-2/1的速度發(fā)散,且2-1的值越大發(fā)散的速度越快,雖然厚尾指數(shù)由小變大時,統(tǒng)計量不再發(fā)散到無窮,但數(shù)值模擬表明仍存在水平扭曲,只是其水平扭曲沒有由大變小時的嚴重。在備則假設既有持久性變點又有厚尾指數(shù)變點時,若12,檢驗勢函數(shù)值得到加強,使得更容易拒絕原假設;而k_1≤k_2時,會削弱檢驗功效。
[Abstract]:As an important research topic in the field of statistics, variable point analysis has always been a hot issue of scholars at home and abroad. In recent twenty years, more and more theories have proved that many economic and financial data show persistent characteristics, and the "peak thick tail" characteristics in financial data can be better depicted by the thick tail sequence. It is very important to study the persistent variation point of the thick tail sequence. In the second chapter, this paper puts forward the method of the truncation test of the persistent variable point of thick tail sequence in the second chapter, to improve the effect of the test potential function. The uniform estimation of the position of the persistent variable points is also obtained. After the truncation, the class variance ratio is robust, that is, its limit distribution is independent of the thick tail exponent, so that it has a good test effect in the case of a small thick tail index. In the third chapter, we study the effect of the thick tail exponential change point on the persistence variable point test in the third chapter. In the case of the original hypothesis, when there is no persistent variable point, but with an exponential change, the thick tail exponent is 12 when the thick tail exponent is smaller, and the higher the value of the 2-1 is diverging. The faster the velocity is, the statistics no longer spread to infinity while the thick tail exponent is larger, but the numerical simulation shows that there is still a horizontal distortion, but the horizontal distortion is not a serious hour. In preparation, if there are both persistent and thick tail exponents, if 12, the test potential function is worth strengthening, making it easier to refuse. The original hypothesis, and k_1 less than k_2, will weaken the efficacy of the test.
【學位授予單位】：西安科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212

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本文編號：1900487