Robust regularized conditional heteroscedastic hidden semi-Markov models for the analysis of sea levels in the Venice Lagoon

This paper introduces a novel robust and regularized modeling framework for analyzing sea-level dynamics in the Venice Lagoon. We propose a conditional heteroscedastic hidden semi-Markov model that captures time-varying exposure to flooding events, accounting for time-varying volatility in a regression framework while explicitly modeling state durations. To enhance estimation stability and interpretability, we incorporate regularization techniques and develop a robust estimation procedure to mitigate the influence of outliers, by considering robust conditional distributions as alternatives to the classical Gaussian distribution. The proposed methodology is applied to hourly sea-level data, revealing distinct temporal conditions associated with observed environmental variables.