請用此 Handle URI 來引用此文件: http://hdl.handle.net/11455/17024
標題: 全球主要股票市場之統計特性
Statistical Properties of Major World Stock Market Indices
作者: 陳怡君
Chun, I-Chun
關鍵字: Stock market
股票市場
Price-price correlation analysis technique
Detrended fluctuation analysis technique (DFA)
Persistence probability
價格對價格的相干分析
去趨勢波動分析(DFA)
持續機率等分析
出版社: 物理學系所
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摘要: 本研究主要目的,是要對全球主要股票市場的統計特性進行研究。在這範圍之研究方法,採用 Log 週期的振盪分析、價格對價格的相干分析、去趨勢波動分析(DFA)、和持續機率等分析。 首先,針對三十個以上的股票市場之低頻數據,其指數演化期間大多超過 10 年以上,數值擬合出持續指數 θp、波動指數 hq、和赫斯特指數 Hq 等;尤其,當 q 值等於 2 時,如眾所周知碎形布朗運動中所描述之赫斯特指數 H2,其值介於零與1之間。其次,對臺灣股票市場之高、低頻數據,其自 1983 年 1 月至 2006 年 5 月期間跨越 20 年以上,使用不同統計分析方法進行研究。研究中探討各國家的股市之統計特性,及與 H2 = 1 − θp 之關係,並比較各國家股票市場間之差異性。 研究結果顯示,持續指數 θp 具有冪定律的行為存在,但其值不完全接近0.5。雖然有些股票市場之持續指數 θp 值接近0.5,同時滿足H2 = 1 − θp 之關係;但是,也有部份股票市場並不滿足此關係。另外,我們也觀察經由 q 階價格對價格的相干函數量化計算,全球主要股票市場顯示出多重碎形的行為存在。 總結來說,我們使用經驗分析對全球主要股票市場之歷史數據作仔細的調查,以發現其統計特性,其動機是要透過多重碎形、赫斯特指數 Hq、波動指數 hq、和持續指數 θp 等觀念,提供能更進一步理解各國股票市場的行為。
In this work, we examine the statistical properties of major world stock market indices. The methodology is formulated using log-periodic financial index oscillation analysis technique, price-price correlation analysis technique, detrended fluctuation analysis technique (DFA), and persistence analysis technique within this scope. First, for the low-frequency data, we present the estimate for three exponents extracted from over thirty stock market indices, in which most financial time series are over ten years. Our studies are based on numerical estimates of the persistence exponent θp, fluctuation exponent hq, and the Hurst exponent Hq. In particular, for q = 2, we recover the fractional Brownian motion case described by the well-known Hurst exponent, 0 < H2 < 1. Furthermore, for both low-frequency data and high-frequency data, we have performed various methods to the Taiwan stock exchange index (TAIEX), spanning over twenty years of data from January 1983 up to May 2006. We compared the values of persistence exponent θp, fluctuation exponent hq, and Hurst exponent Hq among these countries. The relation H2 = 1 − θp among these countries is also discussed. We found that whereas most of the empirical financial stock indices exhibit the universal power law behavior, however, their persistence exponent θp are not all close to 0.5. In some stock market indices, the persistence exponents are close to 0.5 and agree with the relation of θp = 1 − H2. But in other stock market indices, this relation does not hold. We also observed that the financial stocks present the multifractal behavior, which was extracted quantitatively from the qth-order price-price correlation functions. To sum up, we use empirical analyses to investigate the previous data on the major world stock markets carefully to find the statistical characters. Our motivation is to provide a better understanding of major stock markets through the concepts of multifractals, Hurst exponent Hq, fluctuation exponent hq, and persistence exponent θp.
URI: http://hdl.handle.net/11455/17024
其他識別: U0005-1801200816304400
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1801200816304400
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