Analysis and synthetic generation of financial time-series

Financial markets generate large volumes of high-frequency data characterized by volatility, heavy-tailed distributions, non-stationarity, and complex asset dependencies. Accurately modeling and predicting financial time-series is, therefore, challenging yet essential for risk management, algorithmic trading, and market stability. This thesis investigates data-driven approaches for understanding, forecasting, and simulating financial dynamics, with particular emphasis on abrupt market shocks, short-term trend prediction, and multivariate temporal dependencies derived from limit order book (LOB) data. First, a formal framework for stock shock detection and forecasting is introduced, leveraging Lévy-stable modeling and machine learning to anticipate abrupt market movements. Next, a comprehensive benchmark of deep learning models for LOB-based trend prediction reveals significant gaps between experimental performance and real-world generalizability, motivating more robust evaluation practices. To address data scarcity and enable realistic simulations, the thesis proposes generative models that synthesize multivariate time series while preserving correlation dynamics and causal relationships. Finally, it advances robust causal discovery in real-world temporal data exhibiting heavy-tailed behavior. Together, these contributions provide new methodologies and insights for reliable financial time-series analysis, thereby supporting improved risk mitigation, market understanding, and data-driven decision-making.