Optimization of combined time series methods to forecast the demand for coffee in Brazil: A new approach using Normal Boundary Intersection coupled with mixture designs of experiments and rotated factor scores

Abstract

This paper proposed a new multi-objective approach to find the optimal set of weight's combination of forecasts that were jointly efficient with respect to various performance and precision metrics. For this, the residues' series of each previously selected forecasts methods were calculated and, to combine them through of a weighted average, several sets of weights were obtained using Simplex - Lattice Design {m,q}. Then, several metrics were calculated for each combined residues' series. After, Principal Components Factor Analysis (PCFA) was used for extracting a small number series' factor scores to represent the metrics selected with minimal loss of information. The extracted series' factor scores were mathematically modeled with Mixture Design of Experiments (DOE-M). Normal Boundary Intersection method (NBI) was applied to perform joint optimization of these objective functions, allowing to obtain different optimal weights set and the Pareto frontier construction. As selection criteria of the best optimal weights' set were used the Shannon's Entropy Index and Global Percentage Error (GPE). Here, these steps were successfully applied to predict coffee demand in Brazil as a case study. In order to test the applicability and feasibility of the proposed method based on distinct time series, the coffee's Brazilian production and exportation were also foreseen by new method. Besides, the simulated series available in Montgomery et al. (2008) were also used to test the viability of the new method. The results showed that the proposed approach, named of FA-NBI combination method, can be successfully employed to find the optimal weights of a forecasts' combination.