  Self-organized criticality has been claimed to play an important role in many
natural and social systems. In the present work we empirically investigate the
relevance of this theory to stock-market dynamics. Avalanches in stock-market
indices are identified using a multi-scale wavelet-filtering analysis designed
to remove Gaussian noise from the index. Here new methods are developed to
identify the optimal filtering parameters which maximize the noise removal. The
filtered time series is reconstructed and compared with the original time
series. A statistical analysis of both high-frequency Nasdaq E-mini Futures and
daily Dow Jones data is performed. The results of this new analysis confirm
earlier results revealing a robust power law behaviour in the probability
distribution function of the sizes, duration and laminar times between
avalanches. This power law behavior holds the potential to be established as a
stylized fact of stock market indices in general. While the memory process,
implied by the power law distribution of the laminar times, is not consistent
with classical models for self-organized criticality, we note that a power-law
distribution of the laminar times cannot be used to rule out self-organized
critical behaviour.
