We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns.

Introduction Since the 1980s, the deterioration of the academic job market in physics has been attracting a large number of physicists to investment banks: many of them are now working as \quants", designing sophisticated new derivative products or developing numerically intensive data analysis techniques for price and volatility forecasting. More recently, several teams of physicists have launched their own rms, oering services in the elds of nancial software design and forecasting. There exists however another set of motivations { scientic ones { which have also been prompting theoretical physicists { especially those with a background in statistical physics { to become interested in nance. Although this phenomenon may seem a bit mysterious to the outsider, we will attempt to convince the reader that it is not: nancial markets may well be considered as objects of high potential interest for researchers in statistical physics. 1.1 Motivations Statist

We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first present data sources and discuss the choice of a time scale when constructing financial time series. Various statistical properties of asset returns are then described: distributional properties, tail analysis and extreme fluctuations, linear and non-linear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. The last part deals with interest rates: we present some issues encountered in constructing yield curves from empirical data and discuss the statistical properties of the term structure fluctuations.

The Santa Fe Arti cial Stock Market [13, 4] is an agent-based arti-cial model in which agents continually explore and develop expectational models, buy and sell assets based on the predictions of those models that perform best, and con rm or discard these models based on their performance over time. The purpose of this paper is to classify the di erent types of behavior that emerge in the marketasafunctionofevolutionary learning rate, and to explain these emergent behaviors. We observe four di erent types of behavior, which are distinguished by their e ects on the volatility of prices, the complexity ofstrategies, and the wealth earned by agents over time. We also show that the di erences between these behaviors may be attributed to variations in the rate at which agents revise their trading rules and the subsequent types of rules|technical or fundamental|that emerge in the market. 1

The emerging sub#eld of econophysics explores the degree to which certain concepts and methods from statistical physics can be appropriately modi#ed and adapted to provide new insights into questions that have been the focus of interest in the economics community. Here we give a brief overview of two examples of research topics that are receiving recent attention. A #rst topic is the characterization of the dynamics of stock price #uctuations. For example, we investigate the relation between trading activity -- measured by the number of transactions N#t -- and the price change G#t for a given stock, over a time interval [t; t +#t]. We relate the time-dependent standard deviation of price #uctuations -- volatility -- to two microscopic quantities: the number of transactions N#t in #t and the variance W #t of the price changes for all transactions in #t. Our work indicates that while the pronounced tails in the distribution of price #uctuations arise from W#t , the long-range correlations found in |G#t | are largely due to N#t .We also investigate the relation between price #uctuations and the number of shares Q#t traded in #t. We #nd that the distribution of Q#t is consistent with a stable L#evy distribution, suggesting aL#evy scaling relationship between Q#t and N#t , which would provide one explanation for volume-volatility co-movement. A second topic concerns cross-correlations between the price #uctuations of di#erent stocks. We adapt a conceptual framework, random matrix theory (RMT), #rst used in physics to interpret statistical properties of nuclear energy spectra. RMT makes predictions for the statistical properties of matrices that are universal, that is, do not depend on the interactions between the elements comprising the system. In physics systems, deviat...

Abstract—Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.