Empirical probabilistic forecasting: An approach solely based on deterministic explanatory variables for the selection of past forecast errors

Empirical probabilistic forecasts based on out-of-sample forecast errors have the advantage of incorporating all sources of forecast uncertainty but the drawback of being compute-intensive. Hence, selecting the past timestamps for which errors are generated may be crucial in “big data” settings. The existing error-based empirical methods either select errors based on their corresponding point forecasts—not addressing the scalability issue—or do not consider information regarding the target timestamps. We propose an approach solely based on deterministic explanatory variables for selecting past errors, thus exploiting information on the target timestamps without generating any forecasts beforehand. The proposed method was evaluated on the M5 competition’s dataset, compared to the competition’s top 50 submissions and several benchmarks. The results indicate that—given an efficient strategy for selecting past errors—empirical methods can offer a scalable alternative with a performance comparable to the state-of-the-art’s.