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Introduction to hidden Markov models and their application to financial theory
(2025-11-04) Barkolias, Evangelos-Panagiotis; Μπαρκολιάς, Ευάγγελος-Παναγιώτης; Vrontos, Ioannis; Giannakopoulos, Thanasis; Besbeas, Panagiotis
Hidden Markov Models (HMMs) emerged in the late ’60s as a statistical framework designed to extract latent information from data characterized by uncertainty. Their ability to capture hidden structure beyond observable variables soon made them highly relevant for financial applications, where volatility clustering, regime shifts, and non-normality are pervasive. Before turning to empirical application, it is important to first review the theoretical background that underpins HMMs,ensuring a clear understanding of the statistical concepts on which they are built. Building on this foundation, the thesis investigates the modeling of stock returns, beginning with models without temporal dependence and gradually extending to fully Markovian structures, highlighting the crucial role of state dependence in improving both interpretability and predictive power. Methodologically, the research employs Direct Numerical Maximization for parameter estimation and evaluates state sequences. The results show that incorporating state dependence not only improves the statistical characterization of stock return distributions but also yields interpretable latent states corresponding to calm and turbulent regimes. Furthermore, the analysis emphasizes the importance of approaching financial time series from a purely statistical perspective while also ensuring robust optimization and reliable inference.