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    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/111789

    Title: 股票市場中事件發生的尺度性質
    Scaling of Event-Occurrence in Stock Market
    Authors: 施奕甫
    Shih, Yi Fu
    Contributors: 馬文忠
    Ma, Wen Jong
    Shih, Yi Fu
    Keywords: 尺度性質
    Date: 2017
    Issue Date: 2017-08-10 09:59:32 (UTC+8)
    Abstract: 市場股價高高低低,而使股價變動的因素十分多,其中包含股價中隨機的成分,還包括各種因素間的互相影響,以及不同資產間彼此價格的交錯牽動,而如何定量掌握價格變動是重要的課題。我們研究股票市場的整體性。本論文研究從美國S&P500取出的345家公司1996-1999年股價作為研究對象。我們以整體的對數報酬值超過門檻值的一段時間當作一個股價顯著趨勢上升事件或顯著趨勢下降事件研究事件持續的時間長短(超過上界限、低於下界限)持續時間(PERSISTION TIME)和前後兩事件間的時距(又稱等待時間、HITTING TIME、WAITING TIME),我們發現持續時間和等待時間機率密度分布函數為冪次形式函數(POWER LAW)。我們又將各年的數據分成幾個時間區段來看,看事件在每一組中所出現的次數和事件的平均長度及總長度,所得到的時間區段內持續時間總長度的平均及事件次數的平均和計算報酬的時間間隔τ之關係類似對數報酬的尺度不變性。以尺度不變性為背景,並借助隨機過程分析,我們得以獲得不同時間區段中市場漲跌趨勢的訊號。
    There are numerous factors that drive the prices of stocks in a market up and down, including those of stochastic nature and those which interrelate different stocks. It is an important task to effectively quantify the changes in prices of stocks. In our approach, we treat the whole market as an integrated entity. In this thesis, we study the price changes of 345 stocks in S&P500, over the years 1996-1999. We consider the going above(below) the upper(lower) threshold in the overall log-returns of those stocks, for a time span, as an effective up-trend event (down-trend event). We collect the time span of each of those events (persistent time) and that in the idle period between two consecutive events (hitting time)(waiting time). It is found that the probability density functions of the persistent time and of the hitting time follow power laws. In dividing the 4 years into many intervals, we calculate the total persistent time and the event number, over each interval. We found that mean values of these two quantities (total persistent time and event number), averaged over all intervals have power-law dependence on the elapse time t, over which each log-return (difference of log-prices) is calculated. The results suggest we may have a kind of self-similarity in time scales, similar to the well-known scaling property in the log-returns. By taking such scaling properties as the background and with the verification by studying simple models of stochastic processes, we are able to obtain the signature of up-trend and down-trend over the intervals over the four years.
    Reference: [1] Louis Bachelier, “The theory of speculation”, Ann. Sci. Ecole Norm. Super. S’er. 3, 17, 21(1900) .

    [2]M. F. M. Osborne, ”Brownian Motion in the Stock Market” Operations Research 7, pp.145-173(1959) .

    [3] 周煒星,”金融物理學:歷史、現狀與展望”,第四屆中國管理科學與工程論壇(2006).

    [4]Wen-Jong Ma, Shih-Chieh Wang, Chi-Ning Chen, Chin-Kun Hu, “Crossover behavior of Stock returns and mean square displacements of particles governed by the Langevin equation”, EPL , 102, 66003 .(2013).

    [5]王柏淵,1996-1999年美國股票群的收益以高頻日移動平均計算之統計與動力性質分析,國立政治大學應用物理研究所碩士論文(2013) .

    [6] B. F. King, “Market and industry factors in stockprice behavior”J. Bus., 39, 139(1966).

    [7] T. W. Epps, “Comovements in stock prices in the very short run”J. Am. Stat. Assoc., 74, 291 (1979).

    [8]R.N.Mantegna, and H.E. Stanley,”Scaling behavior in the dynamics of an economic index”, Nature 376, 46-49(1995) .

    [9]J. Voit, The Statistical Mechanics of Financial Markets, Third Edition, (Springer. 2005) .

    [10]李育嘉,“漫談布朗運動”,數學傳播第九卷第三期 .

    [11]王帥文,針對股市靜態與動態統計物理量之關聯性研究,國立政治大學應用物理研究所碩士論文(2014) .

    [12]M.P. Beccar Varela – M. Ferraro – S. Jaroszewicz – M.C.Mariani,”Truncated Levy walks applied to the study of the behavior of Market Indices”(2005) .

    [13]R.N. Mantegna, and H.E. Stanley,”Stochastic Process with Ultra –Slow Convergence to a Gaussian The Truncated Levy Flight ”,Phys.Rev.Lett.VOL73,2946(1994) .

    [14]Shaou-Gang Miaou, Jin-Syan Chou, Fundamentals of probability and statistics (高立)(2012) .

    [15]王碩濱,以經濟物理學觀點分析台灣股市日內時間序列,國立東華大學應用物理研究所碩士論文(2006) .

    [16]王子瑜、曹恒光,”布朗運動、朗之萬方程式、與布朗運動學(Brownian Motion, Langevin Equation, and Brownian Dynamics)”,物理雙月刊,廿七卷三期 .

    [17]Aaron Clauset, Cosma Rohilla Shalizi, M. E. J. Newman, “Power-Law Distributions in Empirical Data”, SIAM Review vol51, No.4, pp.661-703(2009) .
    Description: 碩士
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0102755016
    Data Type: thesis
    Appears in Collections:[應用物理研究所 ] 學位論文

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