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Modeling financial markets based on empirical data poses challenges inselecting the most appropriate models. Despite the abundance of empirical dataavailable, researchers often face difficulties in identifying the best-fittingmodel. Long-range memory and self-similarity estimators, commonly used for thispurpose, can yield inconsistent parameter values, as they are tailored tospecific time series models. In our previous work, we explored order disbalancetime series from the broader perspective of fractional L'{e}vy stable motion,revealing a stable anti-correlation in the financial market order flow.However, a more detailed analysis of empirical data indicates the need for amore specific order flow model that incorporates the power-law distribution oflimit order cancellation times. When considering a series in event time, thelimit order cancellation times follow a discrete probability mass functionderived from the Tsallis q-exponential distribution. The combination ofpower-law distributions for limit order volumes and cancellation timesintroduces a novel approach to modeling order disbalance in the financialmarkets. Moreover, this proposed model has the potential to serve as an examplefor modeling opinion dynamics in social systems. By tailoring the model toincorporate the unique statistical properties of financial market data, we canimprove the accuracy of our predictions and gain deeper insights into thedynamics of these complex systems.

Discrete $q$-exponential limit order cancellation time distribution