Multi-criteria Forecast Combination Method with Nonlinear Programming for time series prediction models

Improving prediction computation for time series analysis is still a challenge. Finding a method that combines the benefits of different methodologies is still an open problem. Besides the very efficient prediction combination techniques proposed, there is still a lack of procedures that jointly consider error measure combinations and model constraints. In this work, we propose a new forecast combination procedure based on multi-criteria methods that allows the assignment of weights to different error measures in the objective function and the incorporation of constraints. A real case from the pharmaceutical industry for the sale of a probiotic product is presented to illustrate the performance of the proposal. This method is capable of considering different error measures and non distance based errors, is enriched by the consideration of constraints that consider desirable properties of the solution and is robust with respect to different time series characteristics such as trends, seasonality, etc. Results shows similar accuracy to the best known forecasting methods to date.