本文關(guān)鍵詞：我國(guó)股票指數(shù)的混沌時(shí)間序列分析　出處：《中南大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 混沌時(shí)間序列 相空間重構(gòu) 預(yù)測(cè)

【摘要】：本文以我國(guó)股票市場(chǎng)的兩種股票指數(shù)數(shù)據(jù)作為研究對(duì)象,首先對(duì)這兩種時(shí)間序列進(jìn)行混沌性質(zhì)的判定,得出均為混沌時(shí)間序列,再用混沌預(yù)測(cè)法對(duì)其進(jìn)行預(yù)測(cè)。本文的主要工作安排如下： 第一部分介紹本文用到的基礎(chǔ)知識(shí)與方法。 第二部分對(duì)兩種指數(shù)時(shí)間序列進(jìn)行檢驗(yàn)。首先應(yīng)用功率譜法發(fā)現(xiàn)數(shù)據(jù)結(jié)構(gòu)為非周期運(yùn)動(dòng),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(dòng)性質(zhì)。這三種定性分析法判定這兩組時(shí)間序列都有混沌性質(zhì)。在定性分析的基礎(chǔ)上,再用統(tǒng)計(jì)特征量如Lyapunov指數(shù)、關(guān)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(zhì)。本文采用C-C法進(jìn)行相空間重構(gòu)；G-P算法計(jì)算關(guān)聯(lián)維數(shù)和Kolmogorov熵發(fā)現(xiàn)這兩種序列的關(guān)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(jì)算最大Lyapunov指數(shù),這兩種方法計(jì)算的最大Lyapunov指數(shù)均為正數(shù)；這樣,進(jìn)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(zhì)后,采用局域預(yù)測(cè)法和基于最大Lyapunov指數(shù)預(yù)測(cè)對(duì)兩種序列分別進(jìn)行100步和20步的預(yù)測(cè),并將預(yù)測(cè)值與真實(shí)值進(jìn)行比較,得出方差。結(jié)果表明局域法比之最大Lyapunov指數(shù)法預(yù)測(cè)步數(shù)短,在第一步預(yù)測(cè)和20步預(yù)測(cè)中效果要好于最大Lyapunov指數(shù)法,而后者在100步預(yù)測(cè)中效果好,且其誤差波動(dòng)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(xué)位授予單位】：中南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F832.51;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 門寶輝,趙燮京,梁川;長(zhǎng)江上游川中地區(qū)降水時(shí)間序列的混沌分析[J];長(zhǎng)江科學(xué)院院報(bào);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(xué)報(bào);2000年03期

3 楊正瓴,林孔元;短期負(fù)荷預(yù)測(cè)相空間重構(gòu)法參數(shù)優(yōu)選的數(shù)值測(cè)試與分析[J];電力系統(tǒng)自動(dòng)化;2003年16期

4 馬紅光,韓崇昭,孔祥玉,王國(guó)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(xué)報(bào);2004年04期

5 王海燕,盛昭瀚;混沌時(shí)間序列相空間重構(gòu)參數(shù)的選取方法[J];東南大學(xué)學(xué)報(bào)(自然科學(xué)版);2000年05期

6 簡(jiǎn)相超,鄭君里;一種正交多項(xiàng)式混沌全局建模方法[J];電子學(xué)報(bào);2002年01期

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

8 羅文彬;王海燕;趙林度;;進(jìn)出口總額時(shí)間序列的混沌特性分析及其預(yù)測(cè)[J];工業(yè)技術(shù)經(jīng)濟(jì);2007年01期

9 楊瑞成;王彬;張?zhí)煸?;基于MATLAB的混沌時(shí)間序列算法對(duì)材料腐蝕行為的預(yù)測(cè)[J];蘭州理工大學(xué)學(xué)報(bào);2009年05期

10 湯龍坤;;有噪聲的多維混沌時(shí)序的非線性檢驗(yàn)[J];華僑大學(xué)學(xué)報(bào)(自然科學(xué)版);2006年04期

，

本文編號(hào)：1378327