ProfARIMA: a profit-driven order identification algorithm for ARIMA models in sales forecasting

Abstract

tIn forecasting, evolutionary algorithms are often linked to existing forecasting methods to optimize theirinput parameters. Traditionally, the fitness function of these search heuristics is based on an accuracymeasure. In this paper, however, we combine forecasting accuracy with business expertise by defining aflexible and easily interpretable profit function for sales forecasting, which is based on the profit marginof a given product, the volume of its sales and the accuracy of the forecast. ProfARIMA is a new procedurethat selects the lags of a Seasonal ARIMA model according to the profit of a model’s forecasts by takingadvantage of search heuristics. This procedure is tested on both publicly available datasets and a real-lifeapplication with datasets of The Coca-Cola Company in order to assess its performance, both in profitand accuracy. Three different evolutionary algorithms were implemented during this testing process,i.e. Genetic Algorithms, Particle Swarm Optimization and Simulated Annealing. The results indicate thatProfARIMA always performs at least equally to the Box–Jenkins methodology and often outperformsthis traditional procedure. For The Coca-Cola Company, our new algorithm in combination with GeneticAlgorithms even leads to a significantly larger profit for out-of-sample forecasts.

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ORCID for B. Baesens: orcid.org/0000-0002-5831-5668

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