Title: Long-Term Sequential Prediction Using Expert Advice,
Abstract: 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.