Their complexity stems from two main factors: (i) the interaction of a large number of agents pursuing heterogeneous goals at different time scales through the implementation of trading strategies designed to leverage asymmetric information; (ii) the emergence of selforganizing collective behaviors that do not result from the existence of any central controller and are therefore difficult to anticipate. The concurrence of these aspects contributes to the sporadic and limited-in-time persistence of inefficiencies that make the trading practice profitable. The analysis of existing inefficiencies and the forecasting of new ones is made possible by the mathematical and statistical modeling of the time series reflecting the financial market's behavior. The granularity of these time series widely varies depending on the goal of the analysis, and, in the high-frequency case (i.e., the scenario we are mainly interested in), it can be order-driven with a resolution up to the nanosecond [31]. Indeed, the majority of modern financial exchanges store order-level updates in data structures known as Limit Order Books (LOBs).

We exploit cutting-edge deep learning methodologies to explore the predictability of high-frequency Limit Order Book mid-price changes for a heterogeneous set of stocks traded on the NASDAQ exchange. In so doing, we release `LOBFrame', an open-source code base to efficiently process large-scale Limit Order Book data and quantitatively assess state-of-the-art deep learning models' forecasting capabilities. Our results are twofold. We demonstrate that the stocks' microstructural characteristics influence the efficacy of deep learning methods and that their high forecasting power does not necessarily correspond to actionable trading signals. We argue that traditional machine learning metrics fail to adequately assess the quality of forecasts in the Limit Order Book context. As an alternative, we propose an innovative operational framework that evaluates predictions' practicality by focusing on the probability of accurately forecasting complete transactions. This work offers academics and practitioners an avenue to make informed and robust decisions on the application of deep learning techniques, their scope and limitations, effectively exploiting emergent statistical properties of the Limit Order Book.