本文關鍵詞：我國股票指數(shù)的混沌時間序列分析　出處：《中南大學》2013年碩士論文　論文類型：學位論文

  更多相關文章： 混沌時間序列 相空間重構 預測

【摘要】：本文以我國股票市場的兩種股票指數(shù)數(shù)據(jù)作為研究對象,首先對這兩種時間序列進行混沌性質的判定,得出均為混沌時間序列,再用混沌預測法對其進行預測。本文的主要工作安排如下： 第一部分介紹本文用到的基礎知識與方法。 第二部分對兩種指數(shù)時間序列進行檢驗。首先應用功率譜法發(fā)現(xiàn)數(shù)據(jù)結構為非周期運動,頻數(shù)直方圖分析這兩組數(shù)據(jù)與正態(tài)分布之間存在差異,PCA分析法則表明數(shù)據(jù)為非噪聲序列且具有混動性質。這三種定性分析法判定這兩組時間序列都有混沌性質。在定性分析的基礎上,再用統(tǒng)計特征量如Lyapunov指數(shù)、關聯(lián)維數(shù)與Kolmogorov熵等定量分析判定這兩種指數(shù)的混沌性質。本文采用C-C法進行相空間重構；G-P算法計算關聯(lián)維數(shù)和Kolmogorov熵發(fā)現(xiàn)這兩種序列的關聯(lián)維具有收斂性,Kolmogorov熵為正數(shù)；采用Wolf法和小數(shù)據(jù)量法計算最大Lyapunov指數(shù),這兩種方法計算的最大Lyapunov指數(shù)均為正數(shù)；這樣,進一步說明這兩種指數(shù)序列處于混沌狀態(tài)。 第三部分是在第二部分得出兩種股票指數(shù)數(shù)據(jù)具有混沌性質后,采用局域預測法和基于最大Lyapunov指數(shù)預測對兩種序列分別進行100步和20步的預測,并將預測值與真實值進行比較,得出方差。結果表明局域法比之最大Lyapunov指數(shù)法預測步數(shù)短,在第一步預測和20步預測中效果要好于最大Lyapunov指數(shù)法,而后者在100步預測中效果好,且其誤差波動平緩。
[Abstract]:In this paper, two kinds of stock index data in China's stock market are taken as the research object. Firstly, the chaotic properties of the two time series are determined, and the chaotic time series are obtained. The main work of this paper is as follows: The first part introduces the basic knowledge and methods used in this paper. In the second part, two kinds of exponential time series are tested. Firstly, the power spectrum method is used to find that the data structure is aperiodic, and the frequency histogram is used to analyze the difference between the two groups of data and normal distribution. The PCA analysis rule shows that the data is a non-noise sequence and has the property of mixing. These three qualitative analysis methods determine that the two groups of time series have chaotic properties. On the basis of qualitative analysis. The chaotic properties of the two indices are determined by quantitative analysis such as Lyapunov exponent, correlation dimension and Kolmogorov entropy. In this paper, the phase space reconstruction is carried out by C-C method. When G-P algorithm calculates correlation dimension and Kolmogorov entropy, it is found that the correlation dimension of these two sequences is convergent and Kolmogorov entropy is positive. The maximum Lyapunov exponent is calculated by the Wolf method and the small data method. The maximum Lyapunov exponent calculated by these two methods is both positive. This further shows that the two exponential sequences are in a chaotic state. The third part is in the second part of the two stock index data with chaotic properties. The local prediction method and the prediction based on the maximum Lyapunov exponent were used to predict the two kinds of sequences, and the predicted values were compared with the real values. The results show that the local method has shorter prediction steps than the maximum Lyapunov exponent method and is better than the maximum Lyapunov exponent method in the first step prediction and 20 step prediction. The latter has good effect in 100 step prediction, and its error fluctuation is gentle.
【學位授予單位】：中南大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F832.51;F224

【參考文獻】

相關期刊論文 前10條

1 門寶輝,趙燮京,梁川;長江上游川中地區(qū)降水時間序列的混沌分析[J];長江科學院院報;2004年01期

2 劉昌明,成立;黃河干流下游斷流的徑流序列分析[J];地理學報;2000年03期

3 楊正瓴,林孔元;短期負荷預測相空間重構法參數(shù)優(yōu)選的數(shù)值測試與分析[J];電力系統(tǒng)自動化;2003年16期

4 馬紅光,韓崇昭,孔祥玉,王國華,許劍鋒,朱小菲;基于Lyapunov指數(shù)的非線性模擬電路故障診斷方法[J];電路與系統(tǒng)學報;2004年04期

5 王海燕,盛昭瀚;混沌時間序列相空間重構參數(shù)的選取方法[J];東南大學學報(自然科學版);2000年05期

6 簡相超,鄭君里;一種正交多項式混沌全局建模方法[J];電子學報;2002年01期

7 雷敏,王志中;非線性時間序列的替代數(shù)據(jù)檢驗方法研究[J];電子與信息學報;2001年03期

8 羅文彬;王海燕;趙林度;;進出口總額時間序列的混沌特性分析及其預測[J];工業(yè)技術經(jīng)濟;2007年01期

9 楊瑞成;王彬;張?zhí)煸?;基于MATLAB的混沌時間序列算法對材料腐蝕行為的預測[J];蘭州理工大學學報;2009年05期

10 湯龍坤;;有噪聲的多維混沌時序的非線性檢驗[J];華僑大學學報(自然科學版);2006年04期

，

本文編號：1378327