forecasting Article Comparing Prophet and Deep Learning to ARIMA in Forecasting Wholesale Food Prices Lorenzo Menculini 1, * , Andrea Marini 1 , Massimiliano Proietti 1 , Alberto Garinei 1,2 , Alessio Bozza 3 , Cecilia Moretti 4 and Marcello Marconi 1,2   Citation: Menculini, L.; Marini, A.; Proietti, M.; Garinei, A.; Bozza, A.; Moretti, C.; Marconi, M. Comparing Prophet and Deep Learning to ARIMA in Forecasting Wholesale Food Prices. Forecasting 2021, 3, 644–662. https://doi.org/10.3390/ forecast3030040 Academic Editor: Sonia Leva Received: 16 August 2021 Accepted: 9 September 2021 Published: 15 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: c  2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Idea-re S.r.l., 06128 Perugia, Italy; amarini@idea-re.eu (A.M.); mproietti@idea-re.eu (M.P.) 2 Department of Engineering Sciences, Guglielmo Marconi University, 00193 Rome, Italy; a.garinei@unimarconi.it (A.G.); m.marconi@unimarconi.it (M.M.) 3 Cancelloni Food Service S.p.A., 06063 Magione, Italy; a.bozza@cancelloni.it 4 Independent Researcher, Via Parco 6, 06073 Corciano, Italy; cecilia.moretti1@gmail.com * Correspondence: lmenculini@idea-re.eu Abstract: 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. Keywords: time-series; forecasting; deep learning; ARIMA; prophet; prices; sales 1. Introduction The main aim of firms is profit maximization. To achieve this goal, the constant updating and forecasting of selling prices is of fundamental importance for every company. Although digital transformation is a phenomenon that involves all companies, from small to large, many of them still update prices by hand through logics that are not always clear nor objective and transparent, but rather based on the experience and expertise of those in charge of updating the price list. On the other hand, the automation of price prediction and update can provide a strong productivity boost by freeing up human resources, which can thus be allocated to more creative and less repetitive tasks. This also increases the morale and commitment of employees; it also speeds up the achievement of goals, and improves accuracy by minimizing human errors. Subjectivity is also reduced: once the operating criteria have been established, forecast algorithms will keep behaving consistently. This in turn means an improvement in compliance. Besides the automation of price updates, the prediction of the sales prices charged to customers in the short term also holds great value. In general, organizations across all sectors of industry must undertake business capacity planning to be efficient and com- petitive. Predicting the prices of products is tightly connected to demand forecasting and therefore allows for a better management of warehouse stocks. The current economic crisis caused by COVID-19 has highlighted the value of such management optimization, stressing the importance of the companies’ ability to minimize inventory reserves and just-in-time production models. Forecast models considered in this paper can contribute to keeping the Forecasting 2021, 3, 644–662. https://doi.org/10.3390/forecast3030040 https://www.mdpi.com/journal/forecasting