A Matsuoka‐Based GARMA Model for Environmental and Energy Systems: Theory, Estimation, and Applications

We propose a new time series model for continuous data supported on the open unit interval (0,1)$$ \left(0,1\right) $$, motivated by applications in environmental and energy systems. The Matsuoka autoregressive moving average (MARMA) model combines the Matsuoka distribution‐a uniparametric member of the canonical exponential family‐as the conditional distribution with a flexible ARMA‐type structure for the conditional mean. Parameters are estimated via partial maximum likelihood, allowing for random, time‐dependent covariates and enabling standard asymptotic inference. To construct out‐of‐sample prediction intervals, we explore a bootstrap‐based procedure that captures the uncertainty in the dynamic structure. A simulation study evaluates the finite‐sample performance of the method. The model is applied to the monthly proportion of electricity generated in the United States from all sources, except conventional hydropower. This application highlights the model's utility in capturing serial dependence, ensuring predictions remain within bounds, and providing reliable forecast intervals‐key features for robust energy system planning and environmental policy analysis.