Modeling stochastic inflow patterns to a reservoir with hidden phase-type Markov model Gámiz Pérez, María Luz Montoro Cazorla, Delia Segovia García, María del Carmen Environmental modelling Hidden Markov model Phase-type distributions The authors gratefully acknowledge the constructive comments of two anonymous reviewers, which have greatly improved the manuscript. The authors gratefully acknowledge support from the Spanish Ministry of Science and Innovation - State Research Agency through grant PID2024-156234NB-C22. This work is also supported in part by the IMAG-Maria de Maeztu grant CEX2020-001105-M / AEI / 10.13039/501100011033. We gratefully acknowledge the support and valuable insights provided by Estrella Montoro Cazorla, Operations Manager of the Quiebrajano Dam (Confederación Hidrográfica del Guadalquivir). The hydrological and operational data used in this study were obtained from https://saih.chguadalquivir.es (last accessed on 1 November 2025). This paper proposes a new statistical framework for modelling precipitation patterns in a specific geographical region using Hidden Markov Models (HMMs). Unlike conventional HMMs, where the hidden-state process is Markovian, our approach introduces non-Markovian behaviour by incorporating phase-type distributions to model state durations. This extension allows for a more realistic representation of alternating dry and wet periods, providing deeper insight into the temporal structure of the local climate. Building on this framework, we model reservoir inflow patterns linked to the hidden states and explain observed water storage levels through a Moran model. The analysis uses historical rainfall and inflow records, where inflows are influenced by latent climatic conditions rather than rainfall alone. By integrating these unobserved dynamics, the proposed model captures system complexity that would be missed by direct observationbased modelling. To evaluate performance, we compare our model against several standard ARIMA alternatives. The proposed PH-HMM achieves a substantially lower AIC (204.38) than the best ARIMA specification (211.91) and reduces mean squared error from 185.74 to 183.10. These improvements demonstrate that explicitly modelling regime dynamics yields more accurate and parsimonious representations of inflow processes. Overall, the methodology enhances characterization of underlying climatic regimes and improves inflow modelling, offering a practical tool for water-resource management and climate-adaptation planning. 2026-02-09T08:07:19Z 2026-02-09T08:07:19Z 2025 journal article Gámiz Pérez, M. L.; Montoro Cazorla, D. y Segovia García, M. C. (2025). Modeling stochastic inflow patterns to a reservoir with hidden phase-type Markov model https://hdl.handle.net/10481/110743 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Attribution-NonCommercial-NoDerivatives 4.0 Internacional