Long-Term Sequential Prediction Using Expert Advice

For the prediction with experts' advice setting, we consider some methods to construct forecasting algorithms that suffer loss not much more than any expert in the pool. In contrast to the standard approach, we investigate the case of long-term forecasting of time series. This approach implies that each expert issues a forecast for a time point ahead (or a time interval), and then the master algorithm combines these forecasts into one aggregated forecast (sequence of forecasts). We introduce two new approaches to aggregating experts' long-term interval predictions. Both are based on Vovk's aggregating algorithm. The first approach applies the method of Mixing Past Posteriors method to the long-term prediction. The second approach is used for the interval forecasting and considers overlapping experts. The upper bounds for regret of these algorithms for adversarial case are obtained. We also present the results of numerical experiments on time series long-term prediction.