A novel data-driven dynamic model for inflated doubly-bounded hydro-environmental time series

We introduce the class of inflated Kumaraswamy autoregressive and moving average models for modeling and forecasting hydro-environmental time series that assume values in $[0,1)$ or $(0,1]$. The main goal of our proposal is to handle doubly-bounded times series in the presence of inflated data. Conditioned on past observations, the response variable is assumed to follow an inflated Kumaraswamy (IK) distribution, a composite of continuous and discrete distributions. The Kumaraswamy distribution family is particularly useful for modeling hydro-environmental and related data. In the proposed model, the random component follows the IK distribution, while the systematic component comprises two dynamic structures, one for the conditional median and one for the mixture parameter, the latter being simple and parsimonious. The dynamic structure used for the conditional median encompasses autoregressive and moving average dynamics and allows for the inclusion of regressors. Statistical inference based on conditional maximum likelihood is presented. Results from Monte Carlo simulations based on synthetic hydro-environmental series are used to evaluate the accuracy of inferences in finite sample sizes. Finally, three empirical applications using hydro-environmental data are presented and discussed. They showcase the applicability of the proposed model in the context of data-driven water and environmental management.