Modelling of Heterogeneity and Serial Dependencies in Precipitation Data Using Hidden Markov Models

This paper explores the application of Hidden Markov Models (HMMs) and Finite mixture models (FMMs) for analyzing precipitation data characterized by unobserved heterogeneity, serial dependencies, and unobserved states. Given the significant role of precipitation in agriculture, water resource management, and disaster risk reduction, the study addresses the challenges posed by the nature of precipitation data. We first developed a simulation framework incorporating autoregressive emissions to model distinct hidden states, and later applied the approach to actual rainfall data from the Bungoma region, Kenya. A Gaussian mixture was applied to model the distinct hidden states and HMM was also applied to model the distinct hidden states by taking into account the serial dependencies. The analysis reveals state-dependent variability in precipitation, with distinct mean and variance parameters across states, and highlights the stability of state transitions. For instance, the actual data analysis revealed that we have three distint states with the means(standard deviation); 58.85(28.03), 151.62(43.50) and 215.95(64.06). Model selection criteria based on the BIC indicate the effectiveness of the HMM approach in capturing the broad dynamics of precipitation patterns, providing valuable insights for enhancing climate change adaptation and flood prediction strategies. The results together with pseudo-residuals underscore the potential of HMMs as robust tools for understanding and forecasting precipitation in the context of global climate variability, such as flood predictions, agricultural planning and climate adaptation strategies.