International Day Of Women in Statistics and Data Science

Classical statistical models are built upon an assumption of short-range dependence — an assumption that fails dramatically when confronted with the complexity of real-world aviation datasets. Such datasets routinely exhibit long-range memory, non-stationarity, and heavy-tailed distributions that render conventional approaches inadequate. In this work, we propose a novel fractional statistical framework that draws on advanced operator theory to directly address these challenges, offering both rigorous theoretical guarantees and compelling empirical improvements over established baselines.
We construct a family of Toeplitz-type estimators grounded in the theory of α-fractional Bergman spaces, establish their theoretical properties, validate the framework on a large-scale aviation dataset comprising over 500,000 UAE flight records, and demonstrate prediction error reductions of 23–31% over ARIMA and 14–18% over LSTM-based approaches.