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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. Understanding the financial market as a self-adaptive, strongly interacting system is a real interdisciplinary challenge, where physicists strongly hope to make essential contributions [1,2,3]. The enthusiasm is understandable as the breakthrough of the early 70's in statistical physics taught us how to handle strongly interacting systems with a large number of degrees of freedom. The unbroken development of this and related disciplines brought up several concepts and models like (fractal and multifractal) scaling, frustrated disordered systems, or far from equilibrium phenomena and we have obtained very efficient tools to treat them. Many of us are convinced, that these and similar ideas and techniques will be helpful to understand the mechanisms of the economy. In fact, there have been quite successful attempts along this line [4,5,6]. An ubiquitous aspect of strongly interacting systems is the lack of finite scales. The best understood examples are second order equilibrium phase transitions where renormalization group theory provides a general explanation of scaling and universality [7]. It seems that some features of the stock market can indeed be captured by these concepts: For example, the so called inverse cube law of the distribution of logarithmic returns shows a quite convincing data collapse for different companies with a good fit to an algebraically decaying tail [8,9]. PACSStudies in econophysics concentrate on the possible analogies, although there are important differences between physical and financial systems. This is, of course, a trivial statement -it is enough to refer to the abovementioned self-adaptivity, to the possibility of influencing a

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Records of the traded value of fi stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average : sigma(i) is proportional to alpha, with a strong time scale dependence alpha(Delta(t)). The nontrivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provides information about the microscopic dynamics. We present a set of stylized facts and then show their connection to such behavior. The functional form alpha(Delta(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.

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the "bare" impact these events would have, if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model on the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the jump sizes of future events. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid-ask spread.Keywords: price impact, market orders, limit orders, cancellations, market microstructure, order flow 17 7.3. The final model for small ticks 18 7.4. Interpretation: direct impact vs. induced impact 20 Conclusions 22References 23A. The dependence of the spread on the event flow 24B. Plots of various correlation functions 25