Modified Kumaraswamy seasonal autoregressive moving average models with exogenous regressors for double-bounded hydro-environmental data

This paper proposes the MKSARMAX model for modeling and forecasting time series that can only take on values within a specified range, such as in the interval (0,1). The model is especially good for modeling double-bounded hydro-environmental time series since it accommodates bounded support and asymmetric distribution, making it advantageous compared to the traditional Gaussian-based time series model. The MKSARMAX models the conditional median of a modified Kumaraswamy distributed variable observed over time, by a dynamic structure considering stochastic seasonality and including autoregressive and moving average terms, exogenous regressors, and a link function. The conditional maximum likelihood method is employed to estimate the model parameters. Hypothesis tests and confidence intervals for the parameters of the proposed model are derived using the asymptotic theory of the conditional maximum likelihood estimators. Quantile residuals are defined for diagnostic analysis, and goodness-of-fit tests are subsequently implemented. Synthetic hydro-environmental time series are generated in a Monte Carlo simulation study to assess the finite sample performance of the inferences. Moreover, MKSARMAX outperforms βSARMA, SARMAX, Holt-Winters, and KARMA models in most accuracy measures analyzed when applied to useful water volume datasets, presenting for the first-step forecast at least 98% lower MAE, RMSE, and MAPE values than competitors in the Caconde UV dataset, and 54% lower MAE, RMSE, and MAPE values than competitors in the Guarapiranga UV dataset. These findings suggest that the MKSARMAX model holds strong potential for water resource management. Its flexibility and accuracy in the early forecasting steps make it particularly valuable for predicting flood and drought periods.