Instance-based meta-learning for conditionally dependent univariate multi-step forecasting

Multi-step prediction is a key challenge in univariate forecasting. However, forecasting accuracy decreases as predictions are made further into the future. This is caused by the decreasing predictability and the error propagation along the horizon. In this paper, we propose a novel method called Forecasted Trajectory Neighbors (FTN) for multi-step forecasting with univariate time series. FTN is a meta-learning strategy that can be integrated with any state-of-the-art multi-step forecasting approach. It works by using training observations to correct the errors made during multiple predictions. This is accomplished by retrieving the nearest neighbors of the multi-step forecasts and averaging these for prediction. The motivation is to introduce, in a lightweight manner, a conditional dependent constraint across the forecasting horizons. Such a constraint, not always taken into account by most strategies, can be considered as a sort of regularization element. We carried out extensive experiments using 7795 time series from different application domains. We found that our method improves the performance of several state-of-the-art multi-step forecasting methods. An implementation of the proposed method is publicly available online, and the experiments are reproducible.