Combining Interval Time Series Forecasts. A First Step in a Long Way (Research Agenda)

We observe every day a world more complex, uncertain, and riskier than the world of yesterday. Consequently, having accurate forecasts in economics, finance, energy, health, tourism, and so on; is more critical than ever. Moreover, there is an increasing requirement to provide other types of forecasts beyond point ones such as interval forecasts. After more than 50 years of research, there are two consensuses, “combining forecasts reduces the final forecasting error” and “a simple average of several forecasts often outperforms complicated weighting schemes”, which was named “forecast combination puzzle (FCP)”. The introduction of intervalvalued time series (ITS) concepts and several forecasting methods has been proposed in different papers and gives answers to some big data challenges. Hence, one main issue is how to combine several forecasts obtained for one ITS. This paper proposes some combination schemes with a couple or various ITS forecasts. Some of them extend previous crisp combination schemes incorporating as a novelty the use of Theil’s U. The FCP under the ITS forecasts framework will be analyzed in the context of different accuracy measures and some guidelines will be provided. An agenda for future research in the field of combining forecasts obtained for ITS will be outlined.