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# Mixing past predictions

*Proceedings of the Ninth Symposium on Conformal and Probabilistic Prediction and Applications*, PMLR 128:171-188, 2020.

#### Abstract

In the framework of the theory of prediction with expert advice, we present an algorithm for online aggregation of the functional predictions. The approach implies that at each time step some algorithm issues a forecast in the form of a function and then the master algorithm combines these current and past functional forecasts into one aggregated functional forecast. We apply the proposed algorithm for the problem of long-term predictions of time series. By combining the past and current long-term functional forecasts, we obtain a smoothing mechanism that protects our algorithm from temporary changes in the trend of time series, noise and outliers. To evaluate the performance of presented aggregating algorithm as a long-term forecaster we use a new “integral” loss function and the delayed feedback approach. We apply this algorithm for the regression problems, we present some method for smoothing regression forecasts.