AAPPS Bulletin April 2007
Highlight of the Issue
Analysis and modeling of Complex Time Series
Preface
Chin-Kun Hu, Guest Editor
Modern science started from the establishment of classical mechanics, which owes very much the works of Tycho Brahe (December 14, 1546 – October 24,1601), Johannes Kepler (December 27, 1571 – November 15,1630), and Sir Isaac Newton (25 December 1642 – 20 March 1727).
In late 16th century, Tycho Brahe built large and accurate astronomical instruments first on the island of Hven , then at an observatory near Prague
He took many careful measurements about the motion of planets in the sky. Johannes Kepler was Tycho Brahe's assistant from 1600 until Tycho Brahe's death in October 1601. Kepler inherited Tycho's position and records of planetary motion. Kepler used such data to formulate famous three laws
of planetary motion. On the basis of Kepler's three laws of planetary motion, Newton
The development of classical mechanics is a good example of scientific research: from accurate original data (records of planetary motion) to phenomenological theory (Kepler's three laws of planetary motion), then to fundamental theory of nature (Newton
In comparison with time series for the location of the planet in the sky, the time series of financial markets, physiological signals, or earthquakes is much more complicated. The development in the analysis and modeling of such complex time series is still in the infant stage.
In 1900, French mathematician Louis Bachelier (1870-1946) proposed random walk model for financial time series. After the development of computer science and technology, a great number of financial time series have been recorded. Various methods and ideas have been proposed to analyze or model the financial time series. From distributions of returns and eigenvalue distributions of stock-stock correlation matrix, it has been found that finanical time series does not follow random walk model.
In this special issue of AAPPS Bulletin, we collect some articles about the analysis and modeling of complex financial, physiological, and earthquake time series which were done in Asia Pacific area in recent years.
``What can we learn from analysis of the financial times series?'' by Bing-Hong Wang at University of Science and Technology of China (Hefei) and Shanghai Academy of System Science gives a brief review on the analysis and modeling of financial time series, which were done in his group. Their results show that the returns of Hang Seng index in Hong Kong do not follow the prediction of random walk model.
``Coupled random walks approach to complex financial time series’’ by Wen-Jong Ma at Institute of Physics of Academia Sinica (Taipei) reports a model proposed by Wen-Jong Ma, Chin-Kun Hu, and Ravindra E. Amritkar, which can give correct eigenvalue distribution of stock-stock correlation matrix.
``Multiscale fluctuation analysis of complex signals'' by Ken Kiyono at Nihon University, and Zbigniew R. Struzik and Yoshiharu Yamamoto at The University of Tokyo reports their probability density function (PDF) analysis method and applications of this method to study healthy human heart rates during normal daily life and financial time series before, during and after the occurrence of the Black Monday crash.
``Phase statistics approach to physiological and financial time series'' by Ming-Chya Wu at Research Center for Adaptive Data Analysis of National Central University gives a brief review on the application of empirical mode decomposition and phase statistics to the analysis of physiological and financial time series.
``Event-event correlation in seismicity and aging of aftershocks'' by Sumiyoshi Abe at Mie University and Norikazu Suzuki at Nihon University reports a recent discovery of the aging phenomena and scaling law in complex seismic time series.
The reports of this special issue represent a sampling of the development of a new research field whose further development will affect not only our ideas of the world, but also our life in modern society.
Chin-Kun Hu
Academia Sinica
Email: huck@phys.sinica.edu.tw
Note: This is the Preface of AAPPS Bulletin April 2007 issue on
``Analysis and modeling of Complex Time Series''.
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