  We consider the roughness properties of NYSE (New York Stock Exchange)
stock-price fluctuations. The statistical properties of the data are relatively
homogeneous within the same day but the large jumps between different days
prevent the extension of the analysis to large times. This leads to intrinsic
finite size effects which alter the apparent Hurst (H) exponent. We show, by
analytical methods, that finite size effects always lead to an enhancement of
H. We then consider the effect of fat tails on the analysis of the roughness
and show that the finite size effects are strongly enhanced by the fat tails.
The non stationarity of the stock price dynamics also enhances the finite size
effects which, in principle, can become important even in the asymptotic
regime. We then compute the Hurst exponent for a set of stocks of the NYSE and
argue that the interpretation of the value of H is highly ambiguous in view of
the above results. Finally we propose an alternative determination of the
roughness in terms of the fluctuations from moving averages with variable
characteristic times. This permits to eliminate most of the previous problems
and to characterize the roughness in useful way. In particular this approach
corresponds to the automatic elimination of trends at any scale.

Physics and Society;Statistical Finance