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

Abstract: Accurate forecasts of the US renewable-generation mix are critical for planning transmission upgrades, sizing storage, and setting balancing-market rules. We present a Bayesian Dirichlet ARMA (BDARMA) model for monthly shares of hydro, geothermal, solar, wind, wood, municipal waste, and biofuels from January 2010 to January 2025. The mean vector follows a parsimonious VAR(2) in additive-log-ratio space, while the Dirichlet concentration parameter combines an intercept with ten Fourier harmonics, letting predictive dispersion expand or contract with the seasons. A 61-split rolling-origin study generates twelve-month density forecasts from January 2019 to January 2024. Relative to three benchmarks, a Gaussian VAR(2) in transform space, a seasonal naive copy of last year's proportions, and a drift-free additive-log-ratio random walk, BDARMA lowers the mean continuous ranked probability score by fifteen to sixty percent, achieves component-wise ninety percent interval coverage close to nominal, and matches Gaussian VAR point accuracy through eight months with a maximum loss of 0.02 Aitchison units thereafter. BDARMA therefore delivers sharp, well-calibrated probabilistic forecasts of multivariate renewable-energy shares without sacrificing point precision.