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  • Μικρογραφία εικόνας
    Τεκμήριο
    Distributional forecasting of financial time series using hidden Markov models and Monte Carlo simulation
    (2025-10-07) Fragkakis, Giorgos; Φραγκάκης, Γιώργος; Psarakis, Stelios; Vrontos, Ioannis; Besbeas, Panagiotis
    Financial markets are notoriously complex and ever-shifting, which makes forecasting stock prices a formidable task. By employing sophisticated statistical tools, we can substantially improve our ability to anticipate future price movements. In particular, Hidden Markov Models offer a powerful probabilistic framework for uncovering the latent states, or market regimes, that drive observable market behavior. When trained on historical price series, HMMs can detect these regime changes and capture complex temporal patterns that simpler linear models often miss. More reliable predictions not only deepen our understanding of market dynamics but also equip investors and analysts with more nuanced insights to refine their strategies. This thesis develops and implements a regime-aware forecasting framework for the S&P500 index by combining Hidden Markov Models with Monte Carlo simulation. Initially, an HMM is calibrated using a historical dataset of closing prices to identify the underlying market states and estimate the model parameters, including the state transition matrix and the emission probabilities for each state. Following the successful estimation of the model's parameters, a Monte Carlo simulation is employed to generate a large ensemble of future price trajectories. This simulation-based approach is necessary as obtaining multi-step ahead forecast distributions via direct analytical, closed-form solutions is often intractable for such models. By simulating thousands of possible paths, we construct an empirical distribution for the closing price at each future time horizon. From these distributions, the conditional mean is calculated to serve as the point forecast, while the standard deviation is used to quantify the forecast's uncertainty.