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

arXiv: https://arxiv.org/abs/2202.07955 · HTML: https://mlsanity.com/paper/2202.07955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 16 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [The Splice Bootstrap](https://mlsanity.com/paper/1311.5828/) (2013)

## Abstract (arXiv)

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.