Que será será? The uncertainty estimation of feature-based time series forecasts

Interval forecasts have significant advantages in accounting for the uncertainty estimation of point forecasts, highlighting the importance of providing prediction intervals (PIs) as well as point forecasts in forecasting activities. In this paper, a general feature-based framework is outlined to examine the relationship between time series features and the interval forecasting accuracy and to provide reliable forecasts as well as their uncertainty estimation. Specifically, the framework is divided into training and testing phases. In the training part, we use a collection of time series to train a model to explore how time series features affect the interval forecasting accuracy of different forecasting methods, which makes our proposed framework interpretable in terms of the contribution of each feature to the models' uncertainty prediction. The effect analysis is further applied to assign weights to various benchmark methods with the purpose of reducing the uncertainty of the forecasts. In the testing part, we calculate the point forecasts and PIs of new series using the trained model and weight determination process obtained in the training phase. We illustrate that, whether in point or interval forecasts, our feature-based forecasting framework outperforms all individual benchmark methods and their simple equally weighted combination for different confidence levels on the M3 competition data with an improved computational efficiency.