  Setting sale prices correctly is of great importance for firms, and the study
and forecast of prices time series is therefore a relevant topic not only from
a data science perspective but also from an economic and applicative one. In
this paper we examine different techniques to forecast sale prices applied by
an Italian food wholesaler, as a step towards the automation of pricing tasks
usually taken care by human workforce. We consider ARIMA models and compare
them to Prophet, a scalable forecasting tool by Facebook based on a generalized
additive model, and to deep learning models exploiting Long Short--Term Memory
(LSTM) and Convolutional Neural Networks (CNNs). ARIMA models are frequently
used in econometric analyses, providing a good benchmark for the problem under
study. Our results indicate that ARIMA models and LSTM neural networks perform
similarly for the forecasting task under consideration, while the combination
of CNNs and LSTMs attains the best overall accuracy, but requires more time to
be tuned. On the contrary, Prophet is quick and easy to use, but considerably
less accurate.t overall accuracy, but requires more time to be tuned. On the
contrary, Prophet is quick and easy to use, but considerably less accurate.
