Data-driven algorithm for bottom-up hierarchical forecasting: a global sales forecast for the Coca-Cola Company

Given a set of past data and one or more hierarchies, hierarchical forecasting aims to predict a certain variable on one or multiple levels in that hierarchy. Several frameworks have been developed over the years, which can all be defined by a forecasting model, such as time series analysis, neural networks, etc.., and the direction they forecast in, i.e. top-down, bottom-up or a combination thereof. However, they all take advantage of the structure of the hierarchy in order to achieve the best possible prediction, albeit in different ways. Research has shown that both approaches have already resulted in satisfying error rates on the most local level, but preference for either method depends on the characteristics of the time series and its application. In these practical settings, the main question in hierarchical forecasting is the decision of which level(s) to forecast on, as there are commonly many ways to look at the same data. Our particular application focuses on the sales forecast for The Coca-Cola Company. In the first instance, our goal is to implement an automated model for the company’s global short-term volume forecast, which is the top level of two product hierarchies that they commonly employ. We aim to leverage the double hierarchy by also creating combination levels, allowing for more potential levels to forecast on and aggregate over to achieve the best global prediction. These hierarchies are based on a geographical sales structure and one of the company’s product. Furthermore, we chose to turn to univariate time series models for this case, as we expect a global forecast to undergo little influence from any external factors. This type of model allows for a fast execution as well, which proved to be an essential part of this application in terms of usability within the company. The first central research question of this paper therefore revolves around the data-driven optimization of the algorithm, with regard to the several input parameters, which can be divided into one strategic parameter and four internal model parameters, and with regard to the computation time for the short-term forecast. The strategic parameter involves the prediction horizon of the forecast, which varies between one-month predictions and a year-long forecast. The four internal parameters consist of the use of the hierarchy combination levels, the number of training years for the times series models, the indicator for the best aggregation level and the forecasting method. Concretely, we aim to find the best combination of all of these factors in order to achieve accurate, automated and time-efficient sales predictions. Secondly, for the last input factor of our model, i.e. the forecasting method, we contrast two popular univariate time series models, i.e. Holt-Winters’ triple exponential smoothing and Seasonal ARIMA models. For the latter, we decided to construct a new approach to estimate the model parameters. Because it became apparent that manually estimated ARIMA models performed better than known automated versions, we attempted to formalize our approach by optimizing the parameters according to a combination of performance measures, information criteria and diagnostics by means of a step-wise grid search. We have tested multiple formats of this algorithm and present the most accurate version for our use case in this paper. Our findings indicate that by limiting the input factors, we can achieve accurate, stable and time-efficient global forecasts for both short- and longer-term forecasts. All results are not only evaluated according to their accuracy, but the variance of the remaining errors as well. As a last step, this paper aims to generalize our findings into guidelines for other similar practical applications.status: publishe