Adaptive RF–ARX Ensemble Forecasting of Next-Day PUE with Limited Daily Data

Daily data-center records provide few samples for power usage effectiveness (PUE) forecasting. We evaluate an adaptive combination of random forest (RF) and autoregressive models with exogenous inputs (ARX) for next-day PUE. Both branches predict PUE directly or through shrunken increments and are fitted monthly. The ensemble weight uses errors from the preceding 14 calendar days and is regularized toward equal weighting. An exploratory backtest uses one year of Room 202 records, with 230 evaluated dates from November 2025 to June 2026. The inputs include target-day historical weather downloaded after the study year from Open-Meteo’s Historical Weather API. With a six-month training window, mean absolute error is 0.008336, root mean squared error (RMSE) is 0.013619, and R2 is 0.8606. RMSE is 7.13% below persistence; the paired bootstrap interval for this difference includes zero. With identical branch forecasts, daily weighting reduces RMSE by 3.15% relative to equal weighting and 4.83% relative to monthly updates. Training on all available history gives an RMSE of 0.013348. These estimates apply to the retrospectively assembled inputs and screened records. Separate fan-speed scenarios estimate savings of 12.47–20.63% under assumed fan-energy shares and modeled temperatures.