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28
Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... 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 des ..."
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Cited by 157 (2 self)
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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.
Statistical Properties of Financial Time Series
, 1999
"... 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 ..."
Abstract

Cited by 8 (3 self)
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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 nonlinear 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.
Estimating The Fractal Dimension Of The S&P 500 Index Using Wavelet Analysis
, 2003
"... S&P 500 index data sampled at oneminute 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. ..."
Abstract

Cited by 8 (3 self)
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S&P 500 index data sampled at oneminute 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.
Applied Probability Trust (15 March 2011) HURST INDEX OF FUNCTIONS OF LONG RANGE
"... A positive recurrent, aperiodic Markov chain is said to be long range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous fu ..."
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A positive recurrent, aperiodic Markov chain is said to be long range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the function has the same degree of long range dependence as the chain itself. We illustrate our results through three examples in diverse fields: queuing networks, source compression, and finance.
MARKET MILL DEPENDENCE PATTERN IN THE STOCK MARKET: MULTISCALE CONDITIONAL DYNAMICS
, 810
"... Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditiona ..."
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Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry generating component of the conditional probability distribution result in the ”elementary ” market mill pattern. This asymmetry generating component matches the empirical distribution obtained from the market data. We discuss these properties as a mixture of trendpreserving and contrarian strategies used by market agents. Three basic types of asymmetry patterns characterizing individual stocks are outlined. Multiple time scale considerations make the resulting ”composite ” mill similar to the empirical market mill patterns. Multiscale model also reflects a multiagent nature of the market. 1
Estimating the Fractal Dimension of the S&P 500 Index using Wavelet Analysis
, 2008
"... S&P 500 index data sampled at oneminute 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. An asymptotically unbiased ..."
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S&P 500 index data sampled at oneminute 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. An asymptotically unbiased and efficient estimator using the logscale spectrum is employed. The estimator is asymptotically Gaussian and the variance of the estimate that is obtained from a data segment of N points is of order 1 N. Wavelet analysis is tailor made for the high frequency data set, since it has low computational complexity due to the pyramidal algorithm for computing the detail coefficients. This estimator is robust to additive nonstationarities, and here it is shown to exhibit some degree of robustness to multiplicative nonstationarities, such as seasonalities and volatility persistence, as well. This analysis shows that the market became more efficient in the period 19972000.
MODELING THE INTERACTIVE DRIVERS OF THE STOCK MARKET  A SIMULATIONBASED APPROACH
, 1993
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History of the Efficient Market Hypothesis
, 2011
"... 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 efficie ..."
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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
A DYNAMICAL APPROACH TO STOCK MARKET FLUCTUATIONS
, 2010
"... 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 equatio ..."
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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 equationfree 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 systemnoise 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 “econophysics ” models prove better.
Artificial Intelligence
, 2008
"... 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 agen ..."
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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 corelated 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