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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 339 (4 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.
Nonlinear analysis of cardiac rhythm fluctuations using DFA method
, 1999
"... After a brief overview of classical techniques used to explore cardiac rhythm variability, we show how the DFA method can help diagnose heart failure. Our clinical study reveals that the DFA c coefficient of the cardiac rhythm is an efficient predictor of the future health of patients suffering from ..."
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Cited by 12 (1 self)
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After a brief overview of classical techniques used to explore cardiac rhythm variability, we show how the DFA method can help diagnose heart failure. Our clinical study reveals that the DFA c coefficient of the cardiac rhythm is an efficient predictor of the future health of patients suffering from Congestive Heart Failure. Moreover, we introduce a new coefficient which measures the scale invariance in the cardiac rhythm. This new coefficient appears to be related to the subsequent evolution of the patients.
A multifractal description of wind speed records
 Chaos, Solitons and Fractals
, 2005
"... In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of 1/f α processes with possible long range correlations. The temporal scaling prop ..."
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Cited by 4 (1 self)
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In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of 1/f α processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis MFDFA. It is seen that the records at all four locations exhibit similar scaling behavior which is also reflected in the multifractal spectrum determined under the assumption of a binomial multiplicative cascade model. 1
False EUR Exchange Rates vs. DKK, CHF, JPY and USD. What is a strong currency?
, 2001
"... Abstract. The Euro (EUR) has been a currency introduced by the European Community on Jan. 01, 1999. This implies eleven countries of the European Union which have been found to meet the five requirements of the Maastricht convergence criteria. In order to test EUR behavior and understand various fea ..."
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Abstract. The Euro (EUR) has been a currency introduced by the European Community on Jan. 01, 1999. This implies eleven countries of the European Union which have been found to meet the five requirements of the Maastricht convergence criteria. In order to test EUR behavior and understand various features, we have extrapolated the EUR backwards and therefore have obtained a false euro (FEUR) dating back to 1993. We have derived the exchange rates of the FEUR with respect to several currencies of interest not belonging to the EUR, i.e., Danish Kroner (DKK), Swiss Franc (CHF), Japanese Yen (JPY) and U.S. Dollar (USD). We have first observed the distribution of fluctuations of the exchange rates. Within the Detrended Fluctuation Analysis (DFA) statistical method, we have calculated the power law behavior describing the rootmeansquare deviation of these exchange rate fluctuations as a function of time, displaying in particular the JPY exchange rate case. In order to estimate the role of each currency making the EUR and therefore in view of identifying whether some of them mostly influences its behavior, we have compared the timedependent exponent of the exchange rate fluctuations for EUR with that for the currencies that form the EUR. We have found that the German Mark (DEM) has been leading the fluctuations of EUR/JPY exchange rates, and Portuguese Escudo (PTE) is the farthest away currency from this point of view. 1
Financial Markets as a Complex System: A Short Time Scale Perspective
, 2001
"... In this paper we want to discuss macroscopic and microscopic properties of financial markets. By analyzing quantitatively a database consisting of 13 minute per minute recorded financial time series, we identify some macroscopic statistical properties of the corresponding markets, with a special emp ..."
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In this paper we want to discuss macroscopic and microscopic properties of financial markets. By analyzing quantitatively a database consisting of 13 minute per minute recorded financial time series, we identify some macroscopic statistical properties of the corresponding markets, with a special emphasize on temporal correlations. These analyses are performed by using both linear and nonlinear tools. Multivariate correlations are also tested for, which leads to the identification of a global coupling mechanism between the considered stock markets. The application of a new formalism, called transfer entropy, allows to measure the information flow between some financial time series. We then discuss some key aspects of recent attemps to model financial markets from a microscopic point of view. One model, that is based on the simulation of the order book, is described more in detail, and the results of its practical implementation are presented. We finally address some general aspects of forecasting and modeling, in particular the role of stochastic and nonlinear deterministic processes.
Evidence of crossover phenomena in wind speed data
 IEEE Trans. on Circuits and Systems. Fundam. Theory and Apps
, 2004
"... In this report, a systematic analysis of hourly wind speed data obtained from three potential wind generation sites (in North Dakota) is analyzed. The power spectra of the data exhibited a powerlaw decay characteristic of 1/f α processes with possible longrange correlations. Conventional analysis ..."
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In this report, a systematic analysis of hourly wind speed data obtained from three potential wind generation sites (in North Dakota) is analyzed. The power spectra of the data exhibited a powerlaw decay characteristic of 1/f α processes with possible longrange correlations. Conventional analysis using Hurst exponent estimators proved to be inconclusive. Subsequent analysis using detrended fluctuation analysis (DFA) revealed a crossover in the scaling exponent (α). At short time scales, a scaling exponent of α ∼ 1.4 indicated that the data resembled Brownian noise, whereas for larger time scales the data exhibited long range correlations (α ∼ 0.7). The scaling exponents obtained were similar across the three locations. Our findings suggest the possibility of multiple scaling exponents characteristic of multifractal signals.
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"... quant.iop.org Empirical properties of asset returns: stylized facts and statistical issues ..."
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quant.iop.org Empirical properties of asset returns: stylized facts and statistical issues
Recent daily data of the Southern Oscillation Index have been analyzed. The power spectrum indicates major intrinsic geophysical short periods. We find interesting
, 805
"... 24 days peaks may correspond to the BranstatorKushnir wave, the 27 days may be due to the moon effect rotation, the 37 days peaks is most probably related to the Madden and Julian Oscillation. It is not yet clear the explanations for the 76 days which may be associated with interseasonal oscillatio ..."
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24 days peaks may correspond to the BranstatorKushnir wave, the 27 days may be due to the moon effect rotation, the 37 days peaks is most probably related to the Madden and Julian Oscillation. It is not yet clear the explanations for the 76 days which may be associated with interseasonal oscillation in the tropical atmosphere; the 100 days could be resulting from a mere beat between the 37 and 27 periods, or the 76 and 365 days. Next these periods are used to reconstruct the signal and to produce a forecast for the next 9 months, at the time of writing. After cleansing the signal of those periodicities a detrended fluctuation analysis is performed to reveal the nature of the stochastic structures in the signal and whether specific correlation can be found. We study the evolution of the distribution of first return times, in particular between extreme events. A markedly significant difference from the expected distribution for uncorrelated events is found. Key words: 1