Otimização de modelos SARIMA-DEA com ensembles e delineamento de misturas

Abstract

Accurate forecasting is crucial for several areas of knowledge, such as Economics, Management, Engineering and Statistics. There are several approaches to perform forecasting: time series analysis, regression analysis, artificial neural networks, etc. However, both researchers or analysts must be aware when applying any of the aforementioned techniques because of overfitting – which occurs when a given model has so many parameters that it fits well to the training set, but predicts the test set very poorly. Recently, model combination techniques are widely spread, since the ensemble of models is proven to make the forecast metrics better. However, the overfitting problem may still occur in these cases. To overcome this, this thesis suggests the application of an intermediate step between the selection of models for the ensemble and the optimization of their weights, which is the application of a Data Envelopment Analysis model suitable for the presence of fractional variables so as not to harm the assumption of convexity. To analyze this method, this thesis applies Box & Jenkins models. Therefore, Decision Making Units (DMU) are created through a Complete Factorial Arrangement, modifying the computational parameters. Super-efficiency analysis is applied and the 4 DMUs with the highest efficiency indexes are retained for later combination through Response Surface (RSM) optimization in the context of Mixture Design. It is also proposed the application of multivariate statistical techniques for dimensionality reduction, in order to make the problem computationally smaller. To validate the proposed method, a simulation study was created, comparing the results with the Naive method. The simulation showed that the method proposed in this thesis presents, on average, better results. Finally, the method was applied to series about electricity demand from Brazil and its five geographic regions.