A Comparative Analysis of Prediction Intervals for Forecasting in the Recycling Sector

Sorting materials in the recycling sector involves many sources of uncertainty, making accurate forecasts essential for better decision-making. While point forecasts are widely used, they do not address the inherent uncertainty when predicting future values. Prediction intervals address this issue by providing interval bounds for future values at a prescribed uncertainty level.

In a recycling sector use case, we compare different approaches to construct 80\% and 95\% prediction intervals: We consider (1) two traditional time series forecasting methods – Error, Trend and Seasonality (ETS) and Autoregressive Integrated Moving Average (ARIMA) – with prediction intervals constructed either based on assuming normality of residuals or bootstrapping, and (2) Prediction Intervals utilizing Random Forests (RFs), employing quantile forests, out-of-bag residuals, or one-step boosted forests.

In our use case, prediction intervals constructed under the assumption of normally distributed residuals consistently achieve the prescribed coverage levels but tend to be excessively wide. In contrast, the other methods – particularly the one-step boosted forests – produce narrower intervals while maintaining the prescribed coverage level in most cases.