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| 研究生： |
陳群衛 Chen, Cyun Wei |
|---|---|
| 論文名稱： |
股價波動交互關係的時間特徵 Time characteristic in cross correlation of stock fluctuations |
| 指導教授： |
馬文忠
Ma, Wen Jong |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用物理研究所 Graduate Institute of Applied Physics |
| 論文出版年： | 2015 |
| 畢業學年度： | 103 |
| 語文別： | 英文 |
| 論文頁數： | 65 |
| 中文關鍵詞： | 高頻移動平均 、股市 、卡忽南 -拉維展開式 、指數頻譜 |
| 外文關鍵詞： | HF1MA, Stock, Karhunan-Loeve expansions, Power spectra |
| 相關次數： | 點閱：61 下載：9 |
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本論文在分析 SP500 指數其中交易最為頻繁的 345 家公司在 1996年各月份的股票數據,市場模式的空間特性已經被證實出來[3][4][5],而我們利用卡忽南 -拉維展開來分解股價對數報酬的時間序列, 利用傅立葉分析,並考慮股價對數報酬是否有時間序列重疊,與比較高頻移動平均對時間序列的影響,藉由參考各股市系統的特徵參數來尋找相似或不同之處。
We present the results of our analysis of time series for a collection of 345 stocks listed in S&P 500, to show that integrated information on collective fluctuations in financial data can be revealed quantitatively by combined analysis, focusing separately on either the deterministic or the stochastic contents of the system. In comparing the fluctuations of high frequency one-day moving averages (HF1MA) of the original prices of individual stocks with those inherited in the trajectories of Brownian particles [1], also comparing the log return with overlapping time interval with the log return without overlapping time interval, we can quantify the time characteristic properties of the whole system which would direct the motions of tracer particles. In this study, we decompose the fluctuations in Karhunan-Loeve expansions and reveal the system-specific collective properties by analyzing those collective modes in their time-wise as well as the stock-wise bases, obtained for either the original prices or those of HF1MA, and for the log return with or without overlapping time interval.
Abstract i
Contents ii
List of Figures iv
List of Tables xii
1 Introduction 1
2 Theorem background and Method 3
2.1
Markov process and Stock . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Markov process . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Random walk and Brownian motion . . . . . . . . . . . . . . . . . . . . 5
2.3 Random matrix theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.1 Wishart matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.2 Correlation matrix . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Karhunen-Loeve expansion . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Discrete Fourier Transformation . . . . . . . . . . . . . . . . . . . . . . 9
2.6 High frequency one day moving average . . . . . . . . . . . . . . . . . . 9
3 Data analysis
11
3.1 Definition of log-return . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 The correlation matrix and of Stock price log-return 12
3.3 The eigenvalue and eigenvector distribution of correlation matrix . . . . 13
3.4 The Karhunan-Loeve expansion for temporal part . . . . . . . . . . . . . 20
3.5 Fourier transform of the time-wise part from the Karhunan-Loeve expansion 23
3.6 Power law spectra from log-log scale discrete Fourier transformation . . 31
3.7 Analysis in long time data . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.7.1 Calculation with overlapping . . . . . . . . . . . . . . . . . . . . 38
3.7.2 Calculation without overlapping . . . . . . . . . . . . . . . . . . 52
4 Discussion 60
Bibliography 62
[1] L. BACHELIER. The theory of speculation. Annales scientifiques del Ecole Normale Sup ́erieure, S ́er., pages 21–86, 1900.
[2] Rosario N. Mantegna and H.Eugene Stanley. Scaling behaviour in the dynamics of an economic index. Nature, 376(6):46–49, 1995.
[3] P.Gopikrishnan R.Amaral T.Gurh and H.E.Stanley. Universal and non-universal properties of cross-correlations in financial time series. Phys. Rev. Lett, 1471(83):1471–1474, 1999.
[4] L.Laloux P.Cizeau M Potters and J.Bouchaud. Random matrix theory and financial correlations. Int.J.Theoret. Appl. Finance, 3(3):391–397, 2000.
[5] W.J.MA C.K.HU and Ravindra E. Amritkar. Stochastic dynamical model for stock-stock correlations. PRL, 70(026101), 2004.
[6] W.J.MA S.C.WANG C.N.CHEN and C.K.HU. Crossover behavior of stock returns and mean square displacements of particles governed by the langevin equation. EPL,102(66003), 2013.
[7] Jianbo Gao. Multiscale analysis of complex time series. WILEY, 2007.
[8] Resnick Halliday and Krane. Physics. WILEY, 2002.
[9] A. Einstein. Leipzig. Ann. Phys, 549(17), 1905.
[10] M. L. Mehta. Random Matrices. Academic Press, New York, 1991.
[11] Z.FÜREDI and J. KoMLóS. The eigenvalues of random symmetric matrices. COMBINATORICA 1, (3):233–241, 1981.