Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well known and well researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy to implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series. /// Note: This is the final version of the paper, which appeared in the International Journal of Statistics and Probability. The first draft of this paper was uploaded to Preprints.org on 11 May, 2021: https://doi.org/10.20944/preprints202105.0261.v1 /// Copyrights: This is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).