Weighted sequential hybrid approaches for time series forecasting

Over the past few decades, a large literature has evolved through time series forecasting via combining different individual models by employing various hybrid strategies in order to improve forecasting accuracy. One of the most attractive and extensively-used methodologies, proposed in the literature of time series forecasting is the series methodology in which different components in data are sequentially modeled. In this hybrid methodology, a time series is decomposed to dissimilar components and then appropriate models for each component is used sequentially in order to capture all kind of patterns in data. It means that the output of the first model is used as input of the second model, and the output of the second model is used as input the third model, and so on. Recent literature confirms that the sequential hybrid methodology has become commonplace approach for combining different models and can yield desired accuracy. However, this methodology, despite of all advantages, has some critical assumptions that may degenerate its performance in some specific situations. One of the most essential of these assumptions is that the equal weights are considered for individual components. In other words, the related importance of each component rather than other those components are not considered in calculating procedure of the final hybrid forecasts. In this paper, a novel weighted sequential hybrid model is proposed in order to lift the equal weight assumption in the traditional series hybrid models. In the proposed model, components are first modeled sequentially and then the optimal weight of each component is calculated based on a least square process. It can be theoretically demonstrated that the performance of the proposed model, due to lift the equal weight constraint, will not be worse than traditional sequential hybrid models by same components. Empirical results of four well-known real word benchmark data sets also indicate the effectiveness and appropriateness of the proposed model in comparison to traditional bi-component series hybrid models.