Common scaling patterns in intertrade times of U. S. stocks (original) (raw)
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Scaling and Correlation in Financial Time Series
We discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of ÿnancial time series -(i) The probability distribution of stock price uctuations: Stock price uctuations occur in all magnitudes, in analogy to earthquakesfrom tiny uctuations to very drastic events, such as the crash of 19 October 1987, sometimes referred to as "Black Monday". The distribution of price uctuations decays with a power-law tail well outside the LÃ evy stable regime and describes uctuations that di er by as much as 8 orders of magnitude. In addition, this distribution preserves its functional form for uctuations on time scales that di er by 3 orders of magnitude, from 1 min up to approximately 10 days. (ii) Correlations in ÿnancial time series: While price uctuations themselves have rapidly decaying correlations, the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power-law, persisting for several months. (iii) Volatility and trading activity: We quantify the relation between trading activitymeasured by the number of transactions N t -and the price change G t for a given stock, over a time interval [t; t + t]. We ÿnd that N t displays long-range power-law correlations in time, which leads to the interpretation that the long-range correlations previously found for |G t | are connected to those of N t .
Non-trivial scaling of fluctuations in the trading activity of NYSE
Practical Fruits of Econophysics, 2006
Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -in order to uncover their key features -we have to turn to empirical methods, one of which was recently introduced by Menezes and Barabási. It is based on the observation that for the activity fi(t) of the constituents there is a power law relationship between the standard deviation and the mean value: σi ∝ fi α . For stock market trading activity (traded value), good scaling over 5 orders of magnitude with the exponent α = 0.72 was observed. The origin of this non-trivial scaling can be traced back to a proportionality between the rate of trades N and their mean sizes V . One finds V ∝ N 0.69 for the ∼ 1000 largest companies of New York Stock Exchange. Model independent calculations show that these two types of scaling can be mapped onto each other, with an agreement between the error bars. Finally, there is a continuous increase in α if we look at fluctuations on an increasing time scale up to 20 days.
Physical Review E, 2006
Records of the traded value fi of stocks display fluctuation scaling, a proportionality between the standard deviation σi and the average fi : σi ∝ fi α , with a strong time scale dependence α(∆t). The non-trivial (i.e., neither 0.5 nor 1) value of α may have different origins and provides information about the microscopic dynamics. We present a set of new stylized facts, and then show their connection to such behavior. The functional form α(∆t) originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages, and also display stronger correlations of traded value. The results are integrated into a general framework that can be applied to a wide range of complex systems.
EPL (Europhysics Letters), 2015
We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 min to 10 min. Our study is based on empirical data from the American stock market consisting of tick-by-tick recordings of 31 stocks listed in Dow Jones Industrial Average during the years 2008-2011. Since all the considered quantities except the returns show strong daily patterns related to the variable trading activity in different parts of a day, which are the best evident in the autocorrelation function, we remove these patterns by detrending before we proceed further with our study. We apply the multifractal detrended cross-correlation analysis with sign preserving (MFCCA) and show that the strongest power-law cross-correlations exist between trading activity and volume traded, while the weakest ones exist (or even do not exist) between the returns and the remaining quantities. We also show that the strongest crosscorrelations are carried by those parts of the signals that are characterized by large and medium variance. Our observation that the most convincing power-law cross-correlations occur between trading activity and volume traded reveals the existence of strong fractal-like coupling between these quantities.
A Theory of Large Fluctuations in Stock Market Activity
We propose a theory of large movements in stock market activity. Our theory is motivated by growing empirical evidence on the power-law tailed nature of distributions that characterize large movements of distinct variables describing stock market activity such as returns, volumes, number of trades, and order flow. Remarkably, the exponents that characterize these power laws are similar for different countries, for different types and sizes of markets, and for different market trends, suggesting that a generic theoretical basis may underlie these regularities. Our theory provides a unified way to understand the power-law tailed distributions of these variables, their apparently universal nature, and the precise values of exponents. It links large movements in market activity to the power-law distribution of the size of large financial institutions. The trades made by large financial institutions create large fluctuations in volume and returns. We show that optimal trading by such large institutions generate power-law tailed distributions for market variables with exponents that agree with those found in empirical data. Furthermore, our model also makes a large number of testable out-of-sample predictions.
2009
This paper investigates statistical properties of high-frequency intraday stock returns across various frequencies. Both time series and panel data are employed to explore probability distribution properties, autocorrelations, dynamic conditional correlations, and scaling analysis in the Dow Jones Industrial Average (DJIA) and the NASDAQ intraday returns across 10-minute, 30-monute, 60-minute, 120-minute, and 390-minute frequencies from August 1, 1997, to December 31, 2003. The evidence shows that all of the statistical estimates are highly influenced by the opening returns that contain overnight and non-regular information. The stylized fact of high opening returns generates significant negative (in DJIA) and positive (in NASDAQ) autocorrelations. After excluding the opening intervals, DJIA exhibits a pattern similar to a random walk. While examining the AR(1)-GARCH (1, 1) pattern across both time and frequency variants, we find consistent negative AR(1) at 10-minute and 30-minute ...
Price Fluctuations, Market Activity, and Trading Volume
We investigate the relation between trading activity-measured by the number of trades N t -and the price change G t for a given stock over a time interval [t, t + t]. We relate the time-dependent standard deviation of price changes-volatility-to two microscopic quantities: the number of transactions N t in t and the variance W 2 t of the price changes for all transactions in t. We find that N t displays power-law decaying time correlations whereas W t displays only weak time correlations, indicating that the long-range correlations previously found in |G t | are largely due to those of N t . Further, we analyse the distribution P {N t > x} and find an asymptotic behaviour consistent with a power-law decay. We then argue that the tail-exponent of P {N t > x} is insufficient to account for the tail-exponent of P {G t > x}. Since N t and W t display only weak interdependence, we argue that the fat tails of the distribution P {G t > x} arise from W t , which has a distribution with power-law tail exponent consistent with our estimates for G t . Further, we analyse the statistical properties of the number of shares Q t traded in t, and find that the distribution of Q t is consistent with a Lévy-stable distribution. We also quantify the relationship between Q t and N t , which provides one explanation for the previously observed volume-volatility co-movement.
Size matters: some stylized facts of the stock market revisited
The European Physical Journal B, 2006
We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company capitalization. We show that the second moment of the traded value distribution is finite. Consequently, the Hurst exponents for the corresponding time series can be calculated. These are, however, non-universal: The persistence grows with larger capitalization and this results in a logarithmically increasing Hurst exponent. A similar trend is displayed by intertrade time intervals. Finally, we demonstrate that the distribution of the intertrade times is better described by a multiscaling ansatz than by simple gap scaling.
Scaling of the Distribution of Price Fluctuations of Individual Companies
We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major U.S. stock markets: ͑a͒ the New York Stock Exchange, ͑b͒ the American Stock Exchange, and ͑c͒ the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider ͑i͒ the trades and quotes database, for which we analyze 40 million records for 1000 U.S. companies for the 2-yr period 1994-95; and ͑ii͒ the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16 000 companies in the 35-yr period 1962-96. We study the probability distribution of returns over varying time scales ⌬t, where ⌬t varies by a factor of Ϸ10 5 , from 5 min up to Ϸ4 yr. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent 2.5ϽϰϽ4, well outside the stable Lévy regime 0Ͻ␣Ͻ2. For time scales ⌬t ӷ(⌬t) ϫ Ϸ16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.