The accurate modeling of extreme values in time series data is a critical yet challenging task that has garnered significant interest in recent years. The impact of extreme events on human and natural systems underscores the need for effective and reliable modeling methods. To address this need, we develop novel methods that combine extreme value theory (EVT) with deep neural networks (DNNs) for a range of time series modeling tasks, including forecasting, representation learning, and generative modeling. While integrating EVT into DNNs can provide a robust framework for understanding the behavior of extreme values, several challenges arise in effectively integrating EVT with deep learning architectures. Successfully addressing these challenges necessitates a comprehensive strategy that leverages the strengths of both methodologies. Thus, this thesis posits that integrating extreme value theory within deep learning frameworks offers a sound approach to modeling extreme values in time series data by enhancing forecasting accuracy, advancing representation learning, and improving generative capabilities.This thesis introduces four novel deep learning frameworks: DeepExtrema, Self-Recover, SimEXT, and FIDE, which offer promising solutions for forecasting, imputation, representation learning, and generative modeling of extreme values in time series data. DeepExtrema focuses on integrating extreme value theory with deep learning formulation to improve the accuracy and reliability of extreme events forecasting. Self-Recover addresses data fusion challenges that arise from varying temporal coverage associated with long-term and random missing values of predictors. SimEXT explores how deep learning can be utilized to learn useful time series representations that effectively capture tail distributions for modeling extreme events. FIDE introduces a high-frequency inflation-based conditional diffusion model tailored towards preserving extreme value distributions within generative modeling. These frameworks are evaluated using real-world and synthetic datasets, demonstrating superior performance over existing state-of-the-art methods. The contributions of this research are significant in advancing the field of time series modeling and have practical implications across various domains, such as climate science, finance, and engineering.
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