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

• We study forecasting the critical fractile of a lead time demand distribution when demand is autocorrelated.
• We propose a semi-parametric approach to estimate the critical fractile.
• The proposed approach uses empirical forecast errors to correct a possibly misspecified demand forecasting model.
• We provide conditions for its asymptotic validity and evaluate its small sample performance.

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.