Forecasting the U.S. Renewable-Energy Mix with an ALR-BDARMA Compositional Time-Series Framework

Accurate forecasts of the U.S. renewable energy consumption mix are essential for planning transmission upgrades, sizing storage, and setting balancing market rules. We introduce a Bayesian Dirichlet ARMA model (BDARMA) tailored to monthly shares of hydro, geothermal, solar, wind, wood, municipal waste, and biofuels from January 2010 through January 2025. The mean vector is modeled with a parsimonious VAR(2) in additive log ratio space, while the Dirichlet concentration parameter follows an intercept plus five Fourier harmonics, allowing for seasonal widening and narrowing of predictive dispersion. Forecast performance is assessed with a 61-split rolling origin experiment that issues twelve month density forecasts from January 2019 to January 2024. Compared with three alternatives (a Gaussian VAR(2) fitted in transform space, a seasonal naive approach that repeats last year’s proportions, and a drift-free ALR random walk), BDARMA lowers the mean continuous ranked probability score by 15 to 60 percent, achieves componentwise 90 percent interval coverage near nominal, and maintains point accuracy (Aitchison RMSE) on par with the Gaussian VAR through eight months and within 0.02 units afterward. These results highlight BDARMA’s ability to deliver sharp and well-calibrated probabilistic forecasts for multivariate renewable energy shares without sacrificing point precision.