The Art and Science of Forecast Accuracy Measurement
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1 The Art and Science of Forecast Accuracy Measurement Public Stephan Kolassa, SAP July 06, 2016
2 Disclaimer The information in this presentation is confidential and proprietary to SAP and may not be disclosed without the permission of SAP. Except for your obligation to protect confidential information, this presentation is not subject to your license agreement or any other service or subscription agreement with SAP. SAP has no obligation to pursue any course of business outlined in this presentation or any related document, or to develop or release any functionality mentioned therein. This presentation, or any related document and SAP's strategy and possible future developments, products and or platforms directions and functionality are all subject to change and may be changed by SAP at any time for any reason without notice. The information in this presentation is not a commitment, promise or legal obligation to deliver any material, code or functionality. This presentation is provided without a warranty of any kind, either express or implied, including but not limited to, the implied warranties of merchantability, fitness for a particular purpose, or non-infringement. This presentation is for informational purposes and may not be incorporated into a contract. SAP assumes no responsibility for errors or omissions in this presentation, except if such damages were caused by SAP s intentional or gross negligence. All forward-looking statements are subject to various risks and uncertainties that could cause actual results to differ materially from expectations. Readers are cautioned not to place undue reliance on these forward-looking statements, which speak only as of their dates, and they should not be relied upon in making purchasing decisions SAP SE or an SAP affiliate company. All rights reserved. Public 2
3 Time granularity could be daily, weekly or whatever it doesn t matter What s the best forecast for each series? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 3
4 Which one is the best forecast in each case? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 4
5 Which one is the best forecast in each case? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 5
6 Which one is the best forecast in each case? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 6
7 Which one is the best forecast in each case? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 7
8 Which one is the best forecast in each case? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 8
9 Which one is the best forecast in each case? 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 9
10 Which one is the best forecast in each case? These are simulated time series (Specifically, these are iid Poisson) Therefore, we know the best forecast Unfortunately, best is not well-defined 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 10
11 The expectations (that is, long-term averages) 0.2 The expectations are good candidates for best forecasts In each case, Forecast A is this expectation! 0.4 Forecast B is the median value The median is the middle value 50% of observations are at most the median The median and the expectation differ strongly for low volume count series SAP SE or an SAP affiliate company. All rights reserved. Public 11
12 Does the expected wmape reward forecasts = expectations? wmape = y t y t y t 0.2 Forecast A Forecast B wmape = 164% wmape = 100% 0.4 wmape = 134% wmape = 100% 1.6 wmape = 65% wmape = 63% 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 12
13 What is going on??? 0.2 In each case, the wmape-minimal forecast is lower than the expectation forecast Why? This is actually a mathematical certainty: given any distribution, the median will minimize the expected MAE, wmape and MASE Therefore, minimizing the wmape will yield biased forecasts they are systematically wrong! 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 13
14 Note that the effect is strongest for slowest movers! wmape = y t y t y t 0.2 Forecast A Forecast B wmape = 164% wmape = 100% 0.4 wmape = 134% wmape = 100% 1.6 wmape = 65% wmape = 63% 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 14
15 How about the mean squared error (MSE)? MSE = 1 N y t y t Forecast A Forecast B MSE = 0.20 MSE = MSE = 0.40 MSE = MSE = 1.60 MSE = SAP SE or an SAP affiliate company. All rights reserved. Public 15
16 Or the scaled root mean squared error (srmse)? 0.2 srmse = Forecast A 1 N y t y t 2 1 N y t Forecast B srmse = 2.24 srmse = srmse = 1.58 srmse = srmse = 0.79 srmse = SAP SE or an SAP affiliate company. All rights reserved. Public 16
17 Takeaways Forecast accuracy measurement is not straightforward Common accuracy measures can pull us towards systematically wrong ( biased ) forecasts Mean absolute error (MAE) or mean absolute deviation (MAD) Weighted Mean Absolute Percentage Error (wmape) Mean absolute scaled error (MASE) The effect is strongest for slow movers more problematic if we measure forecast accuracy on finer granularity E.g., daily instead of weekly forecasts Better: use accuracy measures that are minimized by the expectation Mean squared error (MSE) or scaled root mean squared error (srmse) Even better: look at inventories (stock levels and out-of-stock) forecast accuracy is only a means to an end! 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 17
18 Literature On the wmape: Kolassa, S. & Schütz, W. Advantages of the MAD/Mean ratio over the MAPE. Foresight, 2007, 6, On MAE-minimizing forecasts being biased: Morlidge, S. Measuring the Quality of Intermittent Demand Forecasts: It's Worse than We've Thought! Foresight, 2015, 37, Kolassa, S. Evaluating Predictive Count Data Distributions in Retail Sales Forecasting. International Journal of Forecasting, 2016, 32, DOI: /j.ijforecast On the median minimizing the expected MAE: Hanley, J. A.; Joseph, L.; Platt, R. W.; Chung, M. K. & Belisle, P. Visualizing the Median as the Minimum- Deviation Location. The American Statistician, 2001, 55, DOI: / Note that a membership in the International Institute of Forecasters gets you free access to all issues of both Foresight and the IJF a great value for your money! Get a free sample issue of Foresight here 2016 SAP SE or an SAP affiliate company. All rights reserved. Public 18
19 Thank you! Contact information: Stephan Kolassa Research Expert PI ICD IE Consumer Industries SAP (Schweiz) AG High-Tech-Center 2 Bahnstrasse Tägerwilen Switzerland
20 2016 SAP SE or an SAP affiliate company. All rights reserved. No part of this publication may be reproduced or transmitted in any form or for any purpose without the express permission of SAP SE or an SAP affiliate company. SAP and other SAP products and services mentioned herein as well as their respective logos are trademarks or registered trademarks of SAP SE (or an SAP affiliate company) in Germany and other countries. Please see for additional trademark information and notices. Some software products marketed by SAP SE and its distributors contain proprietary software components of other software vendors. National product specifications may vary. These materials are provided by SAP SE or an SAP affiliate company for informational purposes only, without representation or warranty of any kind, and SAP SE or its affiliated companies shall not be liable for errors or omissions with respect to the materials. The only warranties for SAP SE or SAP affiliate company products and services are those that are set forth in the express warranty statements accompanying such products and services, if any. Nothing herein should be construed as constituting an additional warranty. In particular, SAP SE or its affiliated companies have no obligation to pursue any course of business outlined in this document or any related presentation, or to develop or release any functionality mentioned therein. This document, or any related presentation, and SAP SE s or its affiliated companies strategy and possible future developments, products, and/or platform directions and functionality are all subject to change and may be changed by SAP SE or its affiliated companies at any time for any reason without notice. The information in this document is not a commitment, promise, or legal obligation to deliver any material, code, or functionality. All forwardlooking statements are subject to various risks and uncertainties that could cause actual results to differ materially from expectations. Readers are cautioned not to place undue reliance on these forward-looking statements, which speak only as of their dates, and they should not be relied upon in making purchasing decisions SAP SE or an SAP affiliate company. All rights reserved. Public 20
Forecast accuracy measures for count data & intermittent demand Stephan Kolassa International Symposium on Forecasting, June 2015.
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