Statistical Properties of Major World Stock Market Indices

• Main Authors: I-Chun Chun, 陳怡君
• Other Authors: Hsen-Che Tseng
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/75501354491103564695

博士 === 國立中興大學 === 物理學系所 === 96 === 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.