In the retail stage of a food supply chain, food waste and stock-outs occur mainly due to
inaccurate
forecasting of sales which leads to incorrect ordering of products. The time series sales in
food retail industry are characterized by high volatility and skewness, which vary by time. So, the
interval forecasts are required by the retail companies to set appropriate inventory policy
(reorder point or safety stock level). This paper attempts to develop a seasonal autoregressive
integrated moving average with external variables (SARIMAX) model to forecast daily sales of a
perishable food. The process of fitting a SARIMAX model in this study involves: (i) the development
of Seasonal Autoregressive Integrated Moving Average (SARIMA) model and (ii) combining the SARIMA
model and the demand influencing factors using linear regression. As the SARIMAX using multiple
linear regression (SARIMA-MLR) model produces only mean forecast, the possibility of
underestimation and overestimation is very high due to high service level, peak, and sparse sales
in food retail industry. Therefore, a hybrid SARIMA and Quantile Regression (SARIMA-QR) is
developed to construct high and low quantile predictions. Instead of extrapolating the quantiles
from the mean point forecasts of SARIMA-MLR model based on the assumption of normality, the
SARIMA-QR model directly forecasts the quantiles. The developed SARIMA-MLR and SARIMA-QR models
are applied in modeling and forecasting of sales data, i.e., the daily sales of banana from a dis-
count retail store in Lower Bavaria, Germany. The results show that the SARIMA-MLR and -QR models
yield better forecasts at out-sample data when compared to seasonal naïve forecasting, traditional
SARIMA, and multi-layered perceptron neural network (MLPNN) models. Unlike the SARIMA-MLR model,
the SARIMA-QR model provides better prediction intervals and a deep insight into the effects of
demand
influencing factors for different quantiles.