Liquidity and the multiscaling properties of the volume traded on the stock market

– We investigate the correlation properties of transaction data from the New York Stock Exchange. The trading activity fi(t) of each stock i displays a crossover from weaker to stronger correlations at time scales 60− 390 minutes. In both regimes, the Hurst exponent H depends logarithmically on the liquidity of the stock, measured by the mean traded value per minute. All multiscaling exponents τ (q) display a similar liquidity dependence, which clearly indicates the lack of a universal form assumed by other studies. The origin of this behavior is both the long memory in the frequency and the size of consecutive transactions. Financial markets are self-adaptive complex systems and their understanding requires interdisciplinary research, including the application of concepts and tools of statistical physics. The success of modern statistical physics lies to a large extent in explaining phenomena from phase transitions to far-from-equilibrium processes, where the two key concepts have been scaling and universality. When applied to physical systems, both can rely on a solid foundation: renormalization group theory. But how reliable can insights based on these principles be, if we move on to social or economic systems? According to economists, ”physicists [simply] suffer from the belief that there must be universal rules” [1]. The aim of present paper is to point out that the assumption of universality can lead to false conclusions regarding stock market dynamics [2]. We use multifractal analysis – an approach very commonly pursued in econophysics – to point out that the size of the company, or more appropriately the liquidity of its stock, affects the observed characteristics of how it is traded on the market. This dependence is continuous, and therefore it means the absence of universality classes in trading dynamics. By means of multifractal analysis, we show that: (i) Trading activity records show a crossover from weaker to stronger correlations around the time scale of 1 trading day. (ii) (∗) Email: [email protected]