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.

S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January 1989- May 2000) is analyzed, and in particular the Hurst parameter over segments of stationarity (the time period over which the Hurst parameter is almost constant) is estimated.

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 purpose of this paper is to disclose how the Gaussian form of the concept of market efficiency is at the origin of the contemporary professional debate on passive index-linked management which continues on despite the growing popularity of indexing among investment management practitionners in Europe. This particular Gaussian form entered the investment management industry in the 1970’s and carries strong assumptions about the behavior of returns and the structure of the information set. We argue that this ill-defined debate on indexing is due to a confusion between efficiency and Gaussian efficiency. The originality of the paper resides in the point of view choosen as the « main thread ». Instead of focusing on informational issues, now better understood since the seminal paper of Grossman and Stiglitz (1980), we concentrate on the probabilistic aspects included in the testable applications of the concept, so as to connect Fama’s statement of 1970 to Bachelier’s work (Theory of Speculation) of 1900. We establish the link between Bachelier’s dissertation and portfolio management applications of market efficiency. We argue that understanding the precise characteristics of the link associating the informational efficiency concept itself with the underlying probabilistic hypothesis leads to a better approach to

sociology there; he now holds a personal chair. His first book was Statistics in

I am grateful to my supervisor, Wulin Suo, for giving me the opportunity to evaluate the empirical performance of the Black-Scholes Model and the GARCH option pricing model and for his exceptional comments on my manuscript. Also, I dedicate this paper to my family and my love, who always supported and encouraged me in the writing process. ii Table of Contents

Financial market is highly dynamic system for which finding underlying price pattern is highly complex. We have extended the previous work done on automatic stock trading using extended classifier system (XCS) by implementing Q (1) and Q (λ) Reinforcement Learning algorithm. We developed 14 XCS agents using different technical indicators like Moving averages,RSI,CMF,SAR,ADX etc. We showed that by modeling financial prediction as single step reinforcement learning problem and using the concept of delayed reward for checking correctness of action taken, all the benchmarks strategies like buy and hold, 'keeping money in bank ' etc could be beaten. We have also shown that stock price movement is co-related with other day price movement and reformulated the financial forecasting as a multi step process. We introduced the concept of passive set and found that multi step problem formulation gives best results. Q learning gave 18 % better performance than single step reward only RL. Finally we build a portfolio management and optimization system which learns online and does monthly or quarterly rebalancing using the best trader to trade. The results showed that reacting to the market dynamics doesn’t necessarily give us the best result. We showed that such a system give us average performance between the best trader and the worst trader. We

The recent turbulence on the world’s stock markets has reinvigorated the attack on classical economic models of stock market fluctuations. The key problem is determining a dynamic model, which is consistent with observed fluctuations and which reflects investor behavior. Here, we use a novel equation-free approach developed in nonlinear dynamics literature to identify the salient statistical features of fluctuations of the Dow Jones Industrial Average over the past 80 years. We then develop a minimal dynamical model in the form of a stochastic differential equation involving both additive and multiplicative system-noise couplings, which captures these features and whose parameterization on a time scale of days can be used to capture market distributions up to a time scale of months. The terms in the model can be directly linked to “herding” behavior on the part of traders. However, we show that parameters in this model have changed over a number of decades producing different market regimes. This result partially explains how, during some periods of history, “classic ” economic models may work well and at other periods “econo-physics ” models prove better.

A market is said to be efficient with respect to an information set if the price ‘fully reflects ’ that information set, i.e. if the price would be unaffected by revealing the information set to all market participants. The efficient market hypothesis (EMH) asserts that financial markets are efficient. On the one hand, the definitional ‘fully ’ is an exacting requirement, suggesting that no real market could ever be efficient, implying that the EMH is almost certainly false. On the other hand, economics is a social science, and a hypothesis that is asymptotically true puts the EMH in contention for one of the strongest hypotheses in the whole of the social sciences. Strictly speaking the EMH is false, but in spirit is profoundly true. Besides, science concerns seeking the best hypothesis, and until a flawed hypothesis is replaced by a better hypothesis, criticism is of limited value. Starting in the 16th century, this note gives a chronological review of the notable literature relating to the EMH. History of the Efficient Market Hypothesis

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