Date Published: April 3, 2014
Publisher: Public Library of Science
Author(s): Plamen Ch. Ivanov, Ainslie Yuen, Pandelis Perakakis, Matjaž Perc.
We analyse times between consecutive transactions for a diverse group of stocks registered on the NYSE and NASDAQ markets, and we relate the dynamical properties of the intertrade times with those of the corresponding price fluctuations. We report that market structure strongly impacts the scale-invariant temporal organisation in the transaction timing of stocks, which we have observed to have long-range power-law correlations. Specifically, we find that, compared to NYSE stocks, stocks registered on the NASDAQ exhibit significantly stronger correlations in their transaction timing on scales within a trading day. Further, we find that companies that transfer from the NASDAQ to the NYSE show a reduction in the correlation strength of transaction timing on scales within a trading day, indicating influences of market structure. We also report a persistent decrease in correlation strength of intertrade times with increasing average intertrade time and with corresponding decrease in companies’ market capitalization–a trend which is less pronounced for NASDAQ stocks. Surprisingly, we observe that stronger power-law correlations in intertrade times are coupled with stronger power-law correlations in absolute price returns and higher price volatility, suggesting a strong link between the dynamical properties of intertrade times and the corresponding price fluctuations over a broad range of time scales. Comparing the NYSE and NASDAQ markets, we demonstrate that the stronger correlations we find in intertrade times for NASDAQ stocks are associated with stronger correlations in absolute price returns and with higher volatility, suggesting that market structure may affect price behavior through information contained in transaction timing. These findings do not support the hypothesis of universal scaling behavior in stock dynamics that is independent of company characteristics and stock market structure. Further, our results have implications for utilising transaction timing patterns in price prediction and risk management optimization on different stock markets.
The impact of market structure and associated rules of operation on market efficiency and stock price formation have attracted considerable public attention . Developments on the New York Stock Exchange (NYSE) , , have raised the profile of the market operating mechanism, the “market structure”, employed by a stock market. This has also been of concern to those involved in stock market regulation, on behalf of investors , , since optimizing market structure results in more effectively functioning markets  and increases competitiveness for market share in listed stocks . The two major stock markets in the U.S., the NYSE and the National Association of Securities Dealers Automated Quotation System (NASDAQ) National Market have very different structures , , and there is continuing controversy over whether reported differences in stock price behavior are due to differences in market structure or company characteristics . Comparative studies of the NYSE and NASDAQ have primarily focused on stock prices to provide evidence that market organizational structure affects the price formation process , , . It has been shown that stocks registered on the NASDAQ may be characterized by a larger bid-ask spread  and higher price volatility , , . However, this is often attributed to the market capitalization, growth rate or the nature of the companies listed on the NASDAQ . Empirical studies have also emphasized the dominant role and impact of trading volume on prices , ; since traded volume is determined by investors it is difficult to isolate the effects of market structure on price formation. As the influence of market structure on stock prices may be obscured by exogenous factors such as demand and supply , , we hypothesize that modulation of the flow of transactions due to market operations may carry a stronger imprint of the internal market mechanism.
We examine one hundred stocks listed on the NYSE, from eleven industry sectors: Technology-Hardware(5), Semiconductors(2), Pharmaceutical & Medical Equipment(10), Financial(8), Automotive(9), Defense/Aerospace(9), Mining, Metals & Steel Works(8), Chemicals & Plastics(7), Retail & Food(17), Petroleum, Gas & Heavy Machinery(10), Telephone Service Providers(7), Electric & Power Services(8). We study the time intervals between successive stock trades, over a period of four years–4 Jan. 1993 to 31 Dec. 1996–as recorded in the Trades and Quotes (TAQ) database from the NYSE (Table 1).
Like many financial time series the intertrade times (ITT) are inhomogeneous and nonstationary, with statistical properties changing with time, e.g. ITT data exhibit trends superposed on a pattern of daily activity . While ITT fluctuate in an irregular and complex manner on a trade-by-trade basis, empirical observations reveal that periods of inactive trading are often followed by periods of more active trading (Fig. 1). Such patterns can be seen at scales of observation ranging from minutes to months, suggesting that there may be a self-similar, fractal structure in the temporal organisation of intertrade times, independent of the average level of trading activity of a given stock .
We find that the ITT series for all stocks on both markets exhibit long-range power-law correlations over a broad range of time scales, from several trades to hundreds of thousands of trades, characterised by a scaling exponent (Fig. 2 and Fig. 3). For all stocks on both markets we observe a crossover in the scaling curve from a scaling regime with a lower exponent over time scales less than a trading day, to a scaling regime with an exponent (stronger positive correlations) over time scales from days to almost a year.
Understanding the statistical properties of intertrade times and the related underlying mechanism is crucial for the development of more realistic models not only of the flow of transactions –, but more importantly to elucidate (i) the relation between intertrade time dynamics and stock price formation , , –, and (ii) how the process of stock price formation is influenced by market structure. In that context, several prior studies have focused not only on the correlation properties, but also on nonlinear features of intertrade times, and on the functional form of their probability distribution. Early studies reported stretched exponential distributions for intertrade times based on data from a single actively-traded stock over a short period of a few months , , or power-law tailed distributions for rarely-traded 19th century stocks  and eurobonds traded in 1997 . While some of these studies have also considered autocorrelations in intertrade times, they have not identified the functional form of these correlations and whether they are persistent or anti-persistent. A first systematic empirical study based on 30 frequently-traded US stocks over a long period of several years  has (i) reported long-range power-law correlations of persistent type with a characteristic crossover to a superdiffusive behavior at time scales above a trading day, and (ii) identified a Weibull functional form for the distribution of intertrade times. In a follow up study based on a different group of US stocks , the Weibull functional form was also considered a good fit for the intertrade time distribution, with the Tsallis q-exponential form as an alternative. Further investigations considering the intertrade dynamics of a group of frequently-traded Chinese stocks have shown that the Weibull distribution outperforms the Tsallis q-exponential for more than 98.5% of the data . The long-range power law correlations in intertrade times initially reported for US stocks  were also observed for liquid stocks on the Shanghai Stock Exchange . Our results based on 100 NASDAQ and 100 NYSE stocks confirm the presence the long-range power law correlations. The results of these studies, which focus on different markets and different time periods, confirm that the Weibull distribution and long-range power law correlations are stable characteristics of intertrade time dynamics across markets and temporal time scales. Interestingly, similar characteristics were recently reported for commodity dynamics of ancient Babylon (463–72 B.C), and medieval and early modern England (1209–1914 A.D.) markets .