A multi-method forecasting algorithm: Linear unbiased estimation of combine forecast

Abstract

This paper proposes a dynamic ensemble algorithm to combine forecasting results from multiple methodologies subject to their local (recent) predictive performance. In contrast to conventional combination forecasts, the proposed algorithm runs a sparsification process to merge a subset of methodology space to avoid overfitting and improve out-of-sample accuracy. The methodology space consists of various linear and non-linear as well as univariate and multivariate forecasting algorithms frequently used in the literature and industrial practice. The proposed algorithm continuously searches for the best combination to learn models weight. The weights are then used to combine the next forecasting coming from all forecasters. Two empirical studies are presented for illustrating its mechanism and predictive performance: crude oil price forecasting problem and tourist arrival forecasting. Empirical results support the fact that there is no one-fits-all methodology that outperforms in all periods. Our combination algorithm picks a different subset in each step, so the combination structure is dynamically redefined. Although some methodologies perform poorly, and they are never selected for the subset (e.g., ARIMA, ETS), most other methodologies are interchangeably picked or discarded from the combination structure.