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Journal ArticleDOI

Indication of multiscaling in the volatility return intervals of stock markets

29 Jan 2008-Physical Review E (American Physical Society)-Vol. 77, Iss: 1, pp 016109
TL;DR: This work investigates intraday data sets of 500 stocks and finds that the cumulative distribution of return intervals has systematic deviations from scaling, and investigates the moments in the range 10
Abstract: a certain trend with the mean interval . We generate surrogate records using the Schreiber method, and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of . Those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law. We also find that the original and surrogate records exhibit slight tendencies for short and long , due to the discreteness and finite size effects of the records, respectively. To avoid as possible those effects for testing the multiscaling behavior, we investigate the moments in the range 10100, and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks. The distribution of for the surrogate records are very narrow and centered around =0. This suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility.
Citations
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Journal ArticleDOI
TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.
Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

3,647 citations

Journal ArticleDOI
TL;DR: This work analyzes 14,981 daily recordings of the Standard and Poor's (S & P) 500 Index over the 59-year period 1950–2009, and finds power-law cross-correlations between |R| and |R̃| by using detrendedCross-correlation analysis (DCCA), and introduces a joint stochastic process that models these cross-Correlations.
Abstract: In finance, one usually deals not with prices but with growth rates R, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate R, the difference in logarithm between two consecutive values of trading volume. To this end, we use several methods to analyze the properties of volume changes |R|, and their relationship to price changes |R|. We analyze 14,981 daily recordings of the Standard and Poor's (S & P) 500 Index over the 59-year period 1950–2009, and find power-law cross-correlations between |R| and |R| by using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between |R| and |R|, we estimate the tail exponent α of the probability density function P(|R|) ∼ |R|−1−α for both the S & P 500 Index as well as the collection of 1819 constituents of the New York Stock Exchange Composite Index on 17 July 2009. As a new method to estimate α, we calculate the time intervals τq between events where R > q. We demonstrate that τq, the average of τq, obeys τq ∼ qα. We find α ≈ 3. Furthermore, by aggregating all τq values of 28 global financial indices, we also observe an approximate inverse cubic law.

618 citations


Additional excerpts

  • ...The pdf of return intervals Pq(τ) scales with the mean return interval τ as [31–33] Pq(τ) = τ−1f (τ τ )...

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  • ...[33] Wang F et al....

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Journal ArticleDOI
TL;DR: The cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods is surveyed, and the sources ofMultifractality are discussed.
Abstract: Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

185 citations


Cites methods from "Indication of multiscaling in the v..."

  • ...In validating and qualifying the multiscaling behaviour of the recurrence intervals of financial volatility, the relative dependence of recurrence interval moments of different orders of empirical time series has been investigated [234], which is in essence an ESS analysis [235]....

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Journal ArticleDOI
TL;DR: In this article, the authors survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality.
Abstract: Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

154 citations

Posted Content
TL;DR: In this article, the authors show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.
Abstract: We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.

74 citations

References
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Journal ArticleDOI
TL;DR: An overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data can be found in this paper, where several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and pricing of derivative assets, are also discussed.

4,206 citations

Journal ArticleDOI
TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.
Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

3,647 citations

Journal ArticleDOI
TL;DR: In this paper, a Monte-Carlo analysis of stock market returns was conducted and it was found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return also has quite high autocorrelation for long lags.

3,462 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed a theory that concentrated trading patterns arise endogenously as a result of the strategic behavior of liquidity traders and informed traders and provided a partial explanation for some of the recent empitical findings concerning the patterns of volume and price variability in intraday transaction data.
Abstract: This article develops a theory in which concentrated-trading patterns arise endogenously as a result of the strategic behavior of liquidity traders and informed traders. Our results provide a partial explanation for some of the recent empitical findings concerning the patterns of volume and price variability in intraday transaction data. In the last few years, intraday trading data for a number of securities have become available. Several empirical studies have used these data to identify various patterns in trading volume and in the daily behavior of security prices. This article focuses on two of these patterns; trading volume and the variability of returns. Consider, for example, the data in Table 1 concerning shares of Exxon traded during 1981.1 The U-shaped pattern of the average volume of shares traded-namely, the heavy trading in the beginning and the end of the trading day and the relatively light trading in the middle of the day-is very typical and has been documented in a number of studies. [For example,Jain andJoh (1986) examine hourly data for the aggregate volume on the NYSE, which is reported in the Wall StreetJournal, and find the same pattern.] Both the variance of price changes

3,315 citations

Book
01 Jan 2000
TL;DR: Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.
Abstract: This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

2,826 citations


"Indication of multiscaling in the v..." refers background in this paper

  • ...The price dynamics of financial markets has long been a focus of economics and econophysics research [1, 2, 3, 4, 5, 6, 7, 8]....

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