2 research outputs found
Poissonian bursts in e-mail correspondence
Recent work has shown that the distribution of inter-event times for e-mail
communication exhibits a heavy tail which is statistically consistent with a
cascading Poisson process. In this work we extend the analysis to higher-order
statistics, using the Fano and Allan factors to quantify the extent to which
the empirical data depart from the known correlations of Poissonian statistics.
The analysis shows that the higher-order statistics from the empirical data is
indistinguishable from that of randomly reordered time series, thus
demonstrating that e-mail correspondence is no more bursty or correlated than a
Poisson process. Furthermore synthetic data sets generated by a cascading
Poisson process replicate the burstiness and correlations observed in the
empirical data. Finally, a simple rescaling analysis using the best-estimate
rate of activity, confirms that the empirically observed correlations arise
from a non-homogeneus Poisson process
Statistical mixing and aggregation in Feller diffusion
We consider Feller mean-reverting square-root diffusion, which has been
applied to model a wide variety of processes with linearly state-dependent
diffusion, such as stochastic volatility and interest rates in finance, and
neuronal and populations dynamics in natural sciences. We focus on the
statistical mixing (or superstatistical) process in which the parameter related
to the mean value can fluctuate - a plausible mechanism for the emergence of
heavy-tailed distributions. We obtain analytical results for the associated
probability density function (both stationary and time dependent), its
correlation structure and aggregation properties. Our results are applied to
explain the statistics of stock traded volume at different aggregation scales.Comment: 16 pages, 3 figures. To be published in Journal of Statistical
Mechanics: Theory and Experimen