  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 Barabasi. It is based on the observation
that for the activity f_i(t) of the constituents there is a power law
relationship between the standard deviation and the mean value: sigma_i ~
<f_i>^alpha. For stock market trading activity (traded value), good scaling
over 5 orders of magnitude with the exponent alpha = 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 alpha if we look at fluctuations on an increasing time
scale up to 20 days.
