Use of hierarchical models to find the best model to forecast the gallons of regular gasoline demanded in Bogotá (Colombia)

El documento tiene como objetivo encontrar el mejor modelo jerárquico que permita proyectar la demanda total de gasolina corriente y por tanto el recaudo por sobretasa a la gasolina en Bogotá, Colombia, impuesto importante para el financiamiento de la malla vial y sistemas de transporte masivos. Para lograr este objetivo, se emplean datos de los galones reportados por los 6 mayoristas de gasolina corriente de la ciudad bajo dos aproximaciones univariadas (ARIMA y el método de suavizamiento exponencial (ETS por sus siglas en inglés)), cinco métodos y diferentes algoritmos de minimización. Se encuentra que la mejor combinación de estos parámetros para pronosticar los galones de gasolina corriente demandados es el modelo ETS bajo un pronóstico univariado simple.The objective of this analysis is to find the best hierarchical model to forecast the total demand for regular gasoline in Bogotá, Colombia and, therefore, the collection of gasoline surcharges, which is an important tax used to finance road networks and massive transportation systems. We used data reported by 6 wholesalers of regular gasoline in the city, and used two univariate approaches (ARIMA and exponential smoothing (ETS)), five methods and different minimization algorithms to forecast gallons of regular gasoline. Results show that the best combination of these parameters is an ETS model under a simple univariate forecast.Universidad Pablo de Olavid

Prediction of hierarchical time series using structured regularization and its application to artificial neural networks

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that the forecast for an upper-level time series equals the sum of forecasts for corresponding lower-level time series. Previous methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts and then reconciling those forecasts based on their inherent hierarchical structure. With the aim of improving time series predictions, we propose a structured regularization method for completing both phases simultaneously. The proposed method is based on a prediction model for bottom-level time series and uses a structured regularization term to incorporate upper-level forecasts into the prediction model. We also develop a backpropagation algorithm specialized for application of our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate the superiority of our method in terms of prediction accuracy and computational efficiency

Hierarchical forecast reconciliation with machine learning

Hierarchical forecasting methods have been widely used to support aligned decision-making by providing coherent forecasts at different aggregation levels. Traditional hierarchical forecasting approaches, such as the bottom-up and top-down methods, focus on a particular aggregation level to anchor the forecasts. During the past decades, these have been replaced by a variety of linear combination approaches that exploit information from the complete hierarchy to produce more accurate forecasts. However, the performance of these combination methods depends on the particularities of the examined series and their relationships. This paper proposes a novel hierarchical forecasting approach based on machine learning that deals with these limitations in three important ways. First, the proposed method allows for a non-linear combination of the base forecasts, thus being more general than the linear approaches. Second, it structurally combines the objectives of improved post-sample empirical forecasting accuracy and coherence. Finally, due to its non-linear nature, our approach selectively combines the base forecasts in a direct and automated way without requiring that the complete information must be used for producing reconciled forecasts for each series and level. The proposed method is evaluated both in terms of accuracy and bias using two different data sets coming from the tourism and retail industries. Our results suggest that the proposed method gives superior point forecasts than existing approaches, especially when the series comprising the hierarchy are not characterized by the same patterns