For each retail series all admissible ETS models and all ARIMA (pdq PDQ , , ) (, , ) × m models where p and q could take values from
0 to 5, and P and Q could take values from 0 to 2 were applied
using the in-sample period between January 2007 and April 2011
(first 52 observations). The parameters of each model were estimated
by maximizing the likelihood. The ETS model and the ARIMA
model with the minimum value of the AICc that passed the
diagnostic checking were selected for forecasting. The Ljung–Box
test was applied with a significance level of 5% based on the first
15 autocorrelations