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A semi-parametric approach for estimating critical fractiles under autocorrelated demand

Affiliation:	1. Departamento de Estadística, Investigación Operativa y Computación, Universidad de La Laguna, San Cristóbal de La Laguna, Tenerife, Spain;2. Departamento de Estadística, Grupo EFIUCO, Universidad de Córdoba, Córdoba, Spain;3. Ministerio de Ciencia e Innovación, IRNASA – CSIC, Salamanca, Spain;1. Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong;2. Department of Management Science, College of Management, Shenzhen University, Shenzhen 518060, PR China;3. Sino-U.S. Global Logistics Institute, Shanghai Jiao Tong University, Shanghai, PR China;1. Grenoble-INP/UJF-Grenoble 1/CNRS, G-SCOP UMR5272, Grenoble F-38031, France;2. Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, Netherlands;1. DB Schenker Rail Deutschland AG, Rheinstraße 2, D-55116 Mainz, Germany;2. University of Siegen, Hölderlinstraße 3, D-57976 Siegen, Germany;1. Department of Economics, Swedish University of Agricultural Sciences, Box 7013, Johan Brauners väg 3, Uppsala 75007, Sweden;2. Strategic Interaction Group, Max Planck Institute of Economics, Jena, Kahlaische Strasse 10, 07745, Germany;3. Department of Economics, Lund University, Box 7082, Lund 22007, Sweden

Abstract:	Forecasting critical fractiles of the lead time demand distribution is an important problem for operations managers making newsvendor-type inventory decisions. In this paper, we propose a semi-parametric approach to forecasting the critical fractile when demand is serially correlated. Starting from a user-defined but potentially misspecified forecasting model, we use historical demand data to generate empirical forecast errors of this model. These errors are then used to (1) parametrically correct for any bias in the point forecast conditional on the recent demand history and (2) non-parametrically estimate the critical fractile of the demand distribution without imposing distributional assumptions. We present conditions under which this semi-parametric approach provides a consistent estimate of the critical fractile and evaluate its finite sample properties using simulation and real data for retail inventory planning.

Keywords:	Forecasting Newsvendor model Autocorrelated demand Model misspecification Forecast bias Retail operations
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