  A recent analysis of empirical limit order flow data highlights the necessity
for a more refined order flow model that integrates the power-law distribution
of limit order cancellation times. These cancellation times follow a discrete
probability mass function derived from the Tsallis $q$-exponential
distribution, or equivalently, the second form of the Pareto distribution. By
combining fractional L'{e}vy stable motion as the model for limit order inflow
with the power-law distribution for cancellation times, we propose an
innovative approach to modeling order imbalance in financial markets. We extend
this model to a broader context, illustrating its applicability to opinion
dynamics in social systems where opinions have a finite lifespan. This proposed
model exemplifies a stochastic time series characterized by stationary
increments and broken self-similarity. Consequently, it offers a novel
framework for testing methods to evaluate long-range dependence in such time
series.
