A Novel Performance-Based Time Series Forecast Combination Method and Applications with Neural Networks

Performance-based forecast combination approaches determine the weights of the individual forecasts based on the inverse average error for a past time interval. However, although the performances are calculated for a time span, the aim is mostly a one-step-ahead time-point forecast. In these classical methods, a relatively higher prediction error of a single past time-point spreads and decreases the performance value of the model, even though the model is highly successful on other time-points in the interval. In this study, a novel approach is presented where performance of each past time-point prediction is calculated separately. Instead of taking the inverse average error for a pre-determined past time interval, prediction performance is calculated for each past data point separately using the normalized inverse absolute error, then the average performances are calculated for past time interval to get the combination weights. To be able to measure the performance of the presented methodology, it is applied on three well-known time series data. Seven different models of neural networks, based on multi-layer perceptron and extreme learning machines are used to model, forecast and form the combination forecasts. Moreover, four different performance-based combination techniques, two central tendency-based benchmark combination methods and the naïve model are employed for comparison. The obtained results show that proposed methodology is a powerful and robust technique and superior to all performance-based combination techniques compared.