Incorporating hydrometeorological drivers into regime-switching volatility framework for water-level prediction

Abstract

Mathematical modeling plays an important role in probabilistic forecasting and stochastic time-series analysis, particularly for representing hidden states and time-varying volatility. This study develops a regime-switching volatility framework based on a hybrid ARIMAX -Markov Switching GARCH (MS-GARCH) structure for modeling and forecasting water-level fluctuations. The proposed method integrates : (i) structural breakpoint detection to represent nonstationary system transitions, (ii) exogenous hydrometeorological drivers through the ARIMAX model, and (iii) Markovian hidden-state stochastic volatility estimated via likelihood-based optimization. Three families of volatility models, s GARCH , eGARCH , and gjr-GARCH , are evaluated under Normal assumptions to assess the ability to capture regime-dependent hydrological variability. The results show that structural changes substantially influence the underlying volatility process, and may lead to biased probabilistic predictions. In addition, exogenous variables such as rainfall and API were found to influence the conditional mean dynamics of the models. Performance comparisons indicate that the MS-gjr-GARCH model achieved the best overall performance among the evaluated models for heavy-tailed water-level fluctuations and achieved the highest forecasting accuracy among the evaluated models. This study integrates exogenous regression, hidden-state modeling, and stochastic volatility within a unified statistical framework. These findings provide additional insights into flood-related water-level variability and illustrate the value of mathematically grounded statistical models for hydrological forecasting.