Performance metrics for multi-step forecasting measuring win-loss, seasonal variance and forecast stability: an empirical study

Abstract This paper addresses the evaluation of multi-step point forecasting models. Currently, deep learning models for multi-step forecasting are evaluated on datasets by selecting one error metric that is aggregated across the time series and the forecast horizon. This approach hides insights that would otherwise be useful for practitioners when evaluating and selecting forecasting models. We propose four novel metrics to provide additional insights when evaluating models: 1) a win-loss metric that shows how models perform across time series in the dataset , allowing the practitioner to check whether the model is superior for all series or just a subset of series. 2) a variance weighted metric that accounts for differences in variance across the seasonal period. It can be used to evaluate models for seasonal datasets such as rush hour traffic prediction, where it is desirable to select the model that performs best during the periods of high uncertainty. 3) a delta horizon metric measuring how much models update their forecast for a period in the future over the forecast horizon. Less change to the forecast means more stability over time and is desirable for most forecasting applications. 4) decomposed errors that relate the forecasting error to trend, seasonality, and noise. Decomposing the errors allows the practitioners to identify for which components the model is making more errors and adjust the model accordingly. To show the applicability of the proposed metrics, we implement four deep learning architectures and conduct experiments on five benchmark datasets. We highlight several use cases for the proposed metrics and discuss the applicability in light of the empirical results.