Robusti modelli di miscele per la modellazione e il clustering di dati di serie storiche complessi

This cutting-edge thesis explores the potential of mixture models for effectively modeling and clustering complex time series data characterized by skewed distributions, heavy tails, and conditional heteroskedasticity. Traditional models often struggle to capture the inherent characteristics of financial returns, such as asymmetry and non-normality, necessitating the development of more sophisticated techniques. This thesis presents two novel families of mixture models that offer flexible and powerful frameworks for capturing the complexities of financial data. Firstly, a unified approach to enhance the robustness of GARCH models is proposed by incorporating the class of finite mixture of scale mixture of skew normal (SMSN) distributions for component errors. Secondly, a mixture of ARCH (MoARCH) models is introduced, utilizing normal mean-variance mixture (NMVM) distributions. These innovative models provide effective solutions for modeling and analyzing financial data, allowing for more accurate representation and better understanding of its intricacies. The primary contribution of this thesis is a novel approach by augmenting the Generalized Autoregressive Conditional Heteroskedastic (GARCH) process pioneered by Bollerslev (1986) with a scale mixture of skew normal distribution to model financial time series returns. This novel GARCH model surpasses the limitations of traditional approaches and significantly enhances financial modeling and forecasting capabilities. The effectiveness of this methodology is demonstrated through simulations and a real data example using log-returns of Apple stocks from February 1st, 2019, to March 8th, 2022. Additionally, this research introduces the groundbreaking mixture of ARCH model based on NMVM distributions for effective modeling and clustering of time series data. The proposed approach is evaluated using simulated and real-world financial time series data, showcasing its superior accuracy and robustness compared to conventional models when handling skewed and heavy-tailed data. By tackling the challenge of modeling and clustering time series data with skewness and heavy tails, this study addresses prevalent issues encountered in finance, economics, and related fields, where outliers and extreme events greatly impact analysis. The MoARCH models with NMVM distributions present a novel and promising approach for time series classification and clustering tasks. The proposed model is rigorously evaluated using simulated and real-world financial time series data, demonstrating their superior accuracy and robustness, particularly when dealing with skewness, heavy-tails, and conditional heteroskedasticity. These models offer improved decision-making capabilities in diverse domains, including finance, economics, and beyond. Overall, this thesis represents a significant advancement in time series analysis, providing powerful tools for modeling and clustering complex time series data. The novel mixture models overcome the limitations of traditional approaches and offer more accurate and reliable analyses. The findings and insights derived from this research contribute to the development of more robust statistical methods in various fields, opening up new avenues for research and facilitating better decision-making based on a comprehensive understanding of time series data.