Performance of state space and ARIMA models for consumer retail sales forecasting

Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts. HighlightsWe compare the forecasting performance of state space models and ARIMA models.The forecasting performance is demonstrated through a case study of retail sales of women footwear.The model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample.The overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts.Both state space and ARIMA produce coverage probabilities that are very close to the nominal rates.

[1]  T. Lai.  Time series analysis univariate and multivariate methods , 1991 .

[2]  Steven C. Wheelwright,et al.  Forecasting: Methods and Applications, 3rd Edition , 1998 .

[3]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[4]  Robert Fildes,et al.  Against Your Better Judgment? How Organizations Can Improve Their Use of Management Judgment in Forecasting , 2007, Interfaces.

[5]  Rob J Hyndman,et al.  Forecasting with Exponential Smoothing: The State Space Approach , 2008 .

[6]  E. S. Gardner.  EXPONENTIAL SMOOTHING: THE STATE OF THE ART, PART II , 2006 .

[7]  Everette S. Gardner,et al.  Exponential smoothing: The state of the art , 1985 .

[8]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[9]  Mikael Bodén,et al.  Evolving spelling exercises to suit individual student needs , 2007, Appl. Soft Comput..

[10]  Dimitris Mourtzis,et al.  A multi-criteria evaluation of centralized and decentralized production networks in a highly customer-driven environment , 2012 .

[11]  Ashish Garg,et al.  Forecasting women's apparel sales using mathematical modeling , 2003 .

[12]  G. Zhang,et al.  A comparative study of linear and nonlinear models for aggregate retail sales forecasting , 2003 .

[13]  M. Qi,et al.  Forecasting Aggregate Retail Sales: a Comparison of Arti"cial Neural Networks and Traditional Methods , 2001 .

[14]  George Athanasopoulos,et al.  Forecasting: principles and practice , 2013 .

[15]  Janset Kuvulmaz,et al.  Time-Series Forecasting by Means of Linear and Nonlinear Models , 2005, MICAI.

[16]  Xiande Zhao,et al.  Improving the supply chain performance: Use of forecasting models versus early order commitments , 2001 .

[17]  Rob J. Hyndman,et al.  Forecasting with Exponential Smoothing , 2008 .

[18]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[19]  Youqin Pan,et al.  Hybrid Neural Network Model in Forecasting Aggregate U.S. Retail Sales , 2013 .

[20]  Jan Fransoo,et al.  SKU demand forecasting in the presence of promotions , 2009, Expert Syst. Appl..

[21]  G. C. Tiao,et al.  A Course in Time Series Analysis , 2000 .

[22]  Kung-Sik Chan,et al.  Time Series Analysis: With Applications in R , 2010 .

[23]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[24]  Franziska Abend,et al.  State Space Modeling Of Time Series , 2016 .

[25]  Haralambos Sarimveis,et al.  A combined model predictive control and time series forecasting framework for production-inventory systems , 2008 .

[26]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[27]  William W. S. Wei.  Time Series Analysis , 2013 .

[28]  Richard Weber,et al.  Improved supply chain management based on hybrid demand forecasts , 2007, Appl. Soft Comput..

[29]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[30]  David R. Cox,et al.  Time Series Analysis , 2012 .

[31]  M. Stone.  An Asymptotic Equivalence of Choice of Model by Cross‐Validation and Akaike's Criterion , 1977 .

[32]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[33]  Robert H. Shumway,et al.  Time series analysis and its applications : with R examples , 2017 .

[34]  Guoqiang Peter Zhang,et al.  Neural network forecasting for seasonal and trend time series , 2005, Eur. J. Oper. Res..

[35]  Dimitris Mourtzis,et al.  Development of methods and tools for the design and operation of manufacturing networks for mass customisation , 2016 .

[36]  Vijayan Sugumaran,et al.  A Service-Oriented Architecture for Mass Customization—A Shoe Industry Case Study , 2007, IEEE Transactions on Engineering Management.

[37]  Rob J Hyndman,et al.  Automatic Time Series Forecasting: The forecast Package for R , 2008 .

[38]  Yong Yu,et al.  Fashion retail forecasting by evolutionary neural networks , 2008 .

[39]  Sylvain Arlot,et al.  A survey of cross-validation procedures for model selection , 2009, 0907.4728.

[40]  Robert H. Shumway,et al.  Time Series Analysis and Its Applications (Springer Texts in Statistics) , 2005 .

[42]  George E. P. Box,et al.  Time Series Analysis: Box/Time Series Analysis , 2008 .

[43]  Wing-Keung Wong,et al.  A hybrid intelligent model for medium-term sales forecasting in fashion retail supply chains using extreme learning machine and harmony search algorithm , 2010 .

[44]  L. Pazvakawambwa,et al.  Forecasting methods and applications. , 2013 .