Robust Nonparametric Distribution Forecast with Backtest-based Bootstrap and Adaptive Residual Selection

Abstract

Distribution forecast can quantify forecast uncertainty and provide various forecast scenarios with their corresponding estimated probabilities. Accurate distribution forecast is crucial for planning - for example when making production capacity or inventory allocation decisions. We propose a practical and robust distribution forecast framework that relies on backtest-based bootstrap and adaptive residual selection. The proposed approach is robust to the choice of the underlying forecasting model, accounts for uncertainty around the input covariates, and relaxes the independence between residuals and covariates assumption. It reduces the Absolute Coverage Error by more than 63% compared to the classic bootstrap approaches and by 2% - 32% compared to a variety of State-of-the-Art deep learning approaches on in-house product sales data and M4-hourly competition data.