تغییرات زمانی همبستگی های زنجیره ای حجم معاملات در بازار سهام ایالات متحده

Serial correlations in the trading volume of the US stock market are investigated in this paper. The use of the detrended fluctuation analysis implemented within a rolling window indicated that, for the period 1929–2011, the strength of correlations exhibits important temporal variations with a trend shift by the 1990s, and 4-year and 21-year cycles. These empirical findings are compared to those obtained for mature international stock markets (FTSE-100 and Nikkei) and discussed in terms of potential economic and financial implications.

The application of methods from statistical physics to the study of financial markets has provided valuable information on the structure and dynamics of such complex systems. Analyses of returns of individual stocks [1] and [2] and stock indices [3] and [4] have indicated that the cumulative distribution of returns is well fitted by a power-law asymptotic behavior. This pioneering work motivated a plethora of studies oriented to characterize distinctive features of financial and commodity markets. Just for illustration, results included the presence of serial correlations in stock returns [5] and [6], the role of multifractality in the complexity of stock markets [7], the temporal changes of fractality in stock indices [8], the characterization of market dynamics in the vicinity of crashes [9] and many more. The stock return is the most used signal to characterize the dynamics of financial markets. In fact, how the price fluctuation responds to the demand has been widely discussed to understand the origin of large fluctuations of markets [10]. On the other hand, the dynamics of transaction volumes reflect the strength of a market activity as it is related to the excess demand of a specific stock. Studies in this line have focused mainly on establishing the relation between trading volume and volatility/price fluctuations [11], [12], [13], [14] and [15]. Only recently, some work has been oriented to the characterization of the tail statistics of the distribution of volume, which is important in evaluating the validity of different models of market microstructure [16]. It has been found that the number of shares exchanged in a given time interval meets a power-law distribution [17]. High levels of serial correlation in trading volume have also been documented [18], [19] and [20] and attributed to information flow in the market [21] and [22], institutional herding [23] and stealth trading by informed investors [24]. Power-law distribution and serial correlations were also found for the Chinese stock market [25]. Evidence of autocorrelation in daily short volume, which is not explained by liquidity or short-sale constraints, has been found [26]. Based on a proper modification of the DFA [27], cross-correlations between volume change and price change have also been documented for 14 daily recordings of the S&P-500 index over the 59-year period, finding power-law cross-correlations between the absolute volume growth and the absolute price return [28]. In the present study, the scaling properties of trading volume of the US stock market are investigated. By implementing the detrended fluctuation analysis [29] within a rolling window framework, the temporal variations of the scaling exponent are estimated. Serial correlations of the daily trading volume are confirmed and large temporal variations of the correlation strength are found. The presence of structural breaks and 4-year and 21-year cycles in the trading volume correlations are discussed. Comparison with correlations for trading volume of mature international stock markets is performed, suggesting the synchronization of the different stock markets due to, e.g., global trading. The paper is organized as follows. Section 2 provides a brief description of the detrended fluctuation analysis. Section 3 describes and discusses the empirical findings. Section 4 closes the paper with some conclusions.

This work provided further evidence of serial correlations in the trading volume of the US stock market. The usage of a rolling window implementation of the detrended fluctuation analysis has shown that, over the period from 1929 to 2011, correlations exhibit important temporal variations. In the long-term trend, correlations measured in terms of the scaling exponent presented a decrement in the aftermath of the 1987 financial crash. Triggered possibly by the incorporation of professional hedge fund managers in the early 1990s, the trading volume exhibited stronger correlations. The existence of cyclic changes in correlations was also explored, which could be related to the effects of short- and medium-term business cycles.