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Journal ArticleDOI

Common scaling patterns in intertrade times of U. S. stocks

17 May 2004-Physical Review E (Phys Rev E Stat Nonlin Soft Matter Phys)-Vol. 69, Iss: 5, pp 056107-056107
TL;DR: The results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies.
Abstract: We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U.S. economy over a period of 4 yrs. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull distribution, (ii) when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form, (iii) the intertrade times exhibit power-law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales, in agreement with the correlation behavior of the absolute price returns for the corresponding company, and (iv) the magnitude series of intertrade time increments is characterized by long-range power-law correlations suggesting the presence of nonlinear features in the trading dynamics, while the sign series is anticorrelated at small scales. Our results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies. Further, our observation of long-range power-law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock, support the hypothesis that the dynamics of transaction times may play a role in the process of price formation.
Citations
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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


Cites background from "Common scaling patterns in intertra..."

  • ...[34] Ivanov P Ch et al. (2004) Common scaling patterns in intratrade times of U.S. Stocks....

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Journal ArticleDOI
TL;DR: A review of recent empirical and theoretical developments usually grouped under the term Econophysics can be found in this article, where the authors discuss the interactions between physics, mathematics, economics and finance that led to the emergence of Econophysysics.
Abstract: This article and the companion paper aim at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since the name was coined in 1995 by merging the words ‘Economics’ and ‘Physics’, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distribution), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes, etc. We discuss the interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics. We then present empirical studies revealing the statistical properties of financial time series. We begin the presentation with the widely acknowledged ‘stylized facts’, which describe the returns of financial assets—fat tails, volatility clustering, autocorrelation, etc.—and recall that some of these properties are directly linked to the way ‘time’ is taken into account. We continue with the statistical properties observed on order books ...

298 citations

Journal ArticleDOI
TL;DR: It is found that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter, and the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) is investigated.
Abstract: Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an a priori known scaling exponent alpha(0) and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) , and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.

295 citations

Journal ArticleDOI
TL;DR: In this article, a simplified version of the well-scaled transition of CTRW to the diffusive or hydrodynamic limit is presented, and applications of CTRWs to the ruin theory of insurance companies, to growth and inequality processes and to the dynamics of prices in financial markets are outlined and briefly discussed.
Abstract: This paper reviews some applications of continuous time random walks (CTRWs) to Finance and Economics. It is divided into two parts. The first part deals with the connection between CTRWs and anomalous diffusion. In particular, a simplified version of the well-scaled transition of CTRWs to the diffusive or hydrodynamic limit is presented. In the second part, applications of CTRWs to the ruin theory of insurance companies, to growth and inequality processes and to the dynamics of prices in financial markets are outlined and briefly discussed.

260 citations


Cites result from "Common scaling patterns in intertra..."

  • ...[113] confirmed that a stretched-exponential fits well the survival distribution for NYSE stocks as we suggested in Ref....

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Journal ArticleDOI
TL;DR: It is confirmed that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but found differences when focusing on individual users, which may enable a more detailed analysis of the huge body of data contained in the logs of massive users.
Abstract: Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone users of a Chinese mobile phone operator. We confirm that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but find differences when focusing on individual users. We apply statistical tests at the individual level and find that the intercall durations follow a power-law distribution for only 3,460 individuals (3.46%). The intercall durations for the majority (73.34%) follow a Weibull distribution. We quantify individual users using three measures: out-degree, percentage of outgoing calls, and communication diversity. We find that the cell phone users with a power-law duration distribution fall into three anomalous clusters: robot-based callers, telecom fraud, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operators in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cell phone users. We also discover more information about the calling patterns of these four clusters (e.g., the probability that a user will call the cr-th most contact and the probability distribution of burst sizes). Our findings may enable a more detailed analysis of the huge body of data contained in the logs of massive users.

186 citations

References
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Book
01 Jan 1997
TL;DR: In this paper, Campbell, Lo, and MacKinlay present an attempt by three well-known and well-respected scholars to fill an acknowledged void in the empirical finance literature, a text covering the burgeoning field of empirical finance.
Abstract: This book is an ambitious effort by three well-known and well-respected scholars to fill an acknowledged void in the literature—a text covering the burgeoning field of empirical finance. As the authors note in the preface, there are several excellent books covering financial theory at a level suitable for a Ph.D. class or as a reference for academics and practitioners, but there is little or nothing similar that covers econometric methods and applications. Perhaps the closest existing text is the recent addition to the Wiley Series in Financial and Quantitative Analysis. written by Cuthbertson (1996). The major difference between the books is that Cuthbertson focuses exclusively on asset pricing in the stock, bond, and foreign exchange markets, whereas Campbell, Lo, and MacKinlay (henceforth CLM) consider empirical applications throughout the field of finance, including corporate finance, derivatives markets, and market microstructure. The level of anticipation preceding publication can be partly measured by the fact that at least three reviews (including this one) have appeared since the book arrived. Moreover, in their reviews, both Harvey (1998) and Tiso (1998) comment on the need for such a text, a sentiment that has been echoed by numerous finance academics.

7,169 citations


"Common scaling patterns in intertra..." refers background in this paper

  • ...Investigations of price dynamics of financial assets and indices have long been the key focus of economic research [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]....

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  • ...[7] J....

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  • ...Recent studies, however, have turned to the information offered by other aspects of the trading process such as volume of shares traded at each transaction [24, 25] or number of trades in a unit time [26, 27], and their possible relation to price formation [7, 28, 29, 30, 31]....

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Book
20 Nov 2000
TL;DR: In this paper, the authors present an exact solvable model of coalescence and the IPDF method to represent the dynamics of random walks and diffusion in the Sierpinski gasket.
Abstract: Preface Part I. Basic Concepts: 1. Fractals 2. Percolation 3. Random walks and diffusion 4. Beyond random walks Part II. Anomalous Diffusion: 5. Diffusion in the Sierpinski gasket 6. Diffusion in percolation clusters 7. Diffusion in loopless structures 8. Disordered transition rates 9. Biased anomalous diffusion 10. Excluded-volume interactions Part III. Diffusion-Limited Reactions: 11. Classical models of reactions 12. Trapping 13. Simple reaction models 14. Reaction-diffusion fronts Part IV. Diffusion-Limited Coalescence: An Exactly Solvable Model: 15. Coalescence and the IPDF method 16. Irreversible coalescence 17. Reversible coalescence 18. Complete representations of coalescence 19. Finite reaction rates Appendix A. Fractal dimension Appendix B. Number of distinct sites visited by random walks Appendix C. Exact enumeration Appendix D. Long-range correlations References Index.

972 citations


Additional excerpts

  • ...[46] D....

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  • ...The scaling or correlation exponent α is related to the autocorrelation function exponent γ (C(n) ∼ n when 0 < γ < 1) and to the power spectrum exponent β (S(f) ∼ 1/f) by α = 1 − γ/2 = (β + 1)/2 [43, 46]....

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Book
14 May 2001
TL;DR: In this paper, a unified view of high frequency time series methods is presented, with particular emphasis on foreign exchange markets, as well as currency, interest rate, and bond futures markets.
Abstract: Liquid markets generate hundreds or thousands of ticks (the minimum change in price a security can have, either up or down) every business day. Data vendors such as Reuters transmit more than 275,000 prices per day for foreign exchange spot rates alone. Thus, high-frequency data can be a fundamental object of study, as traders make decisions by observing high-frequency or tick-by-tick data. Yet most studies published in financial literature deal with low frequency, regularly spaced data. For a variety of reasons, high-frequency data are becoming a way for understanding market microstructure. This book discusses the best mathematical models and tools for dealing with such vast amounts of data. This book provides a framework for the analysis, modeling, and inference of high frequency financial time series. With particular emphasis on foreign exchange markets, as well as currency, interest rate, and bond futures markets, this unified view of high frequency time series methods investigates the price formation process and concludes by reviewing techniques for constructing systematic trading models for financial assets.

968 citations

Book
01 Jan 2008
TL;DR: This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical interference for extreme values and additional sections and chapters, elaborated on more than 100 pages, are particularly concerned with topics like dependencies, the conditional analysis and the multivariate modeling of extreme data.
Abstract: * Updated for the Third Edition, and expanded by some 100 pages * New chapters include An Overview of Reduced-Bias Estimation; The Spectral Decomposition Methodology; About Tail Independence; and Extreme Value Statistics of Dependent Random Variables * Includes CD-ROM with statistical program Academic Xtremes 4.1, and StatPascal The statistical analysis of extreme data is important for various disciplines, including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical interference for extreme values. The entire text of this third edition has been thoroughly updated and rearranged to meet the new requirements. Additional sections and chapters, elaborated on more than 100 pages, are particularly concerned with topics like dependencies, the conditional analysis and the multivariate modeling of extreme data. Parts I–III about the basic extreme value methodology remain unchanged to some larger extent, yet notable are, e.g., the new sections about "An Overview of Reduced-Bias Estimation" (co-authored by M.I. Gomes), "The Spectral Decomposition Methodology", and "About Tail Independence" (co-authored by M. Frick), and the new chapter about "Extreme Value Statistics of Dependent Random Variables" (co-authored by H. Drees). Other new topics, e.g., a chapter about "Environmental Sciences", (co--authored by R.W. Katz), are collected within Parts IV–VI.

555 citations

Book
01 Jan 2000
TL;DR: In this article, the authors introduce the concepts of probability theory, extreme risks and optimal portfolios, and futures and options: fundamental concepts, and some more specific problems, including options: some specific problems.
Abstract: 1. Probability theory: basic notions 2. Statistics of real prices 3. Extreme risks and optimal portfolios 4. Futures and options: fundamental concepts 5. Options: some more specific problems Glossary.

551 citations


"Common scaling patterns in intertra..." refers background in this paper

  • ...[16] J....

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  • ...These features suggest that information may be contained in the structure and temporal organization of trading activity, and that a close analysis of trading dynamics may offer quantitative insight into the complex mechanism driving price fluctuations [16, 28]....

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  • ...Investigations of price dynamics of financial assets and indices have long been the key focus of economic research [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]....

    [...]