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# Aggregating strategies for long-term forecasting

*Proceedings of the Seventh Workshop on Conformal and Probabilistic Prediction and Applications*, PMLR 91:63-82, 2018.

#### Abstract

The article is devoted to investigating an application of aggregating algorithms to the problem of the long-term forecasting. We examine the classic aggregating algorithms based on the exponential reweighing. For the general Vovk’s aggregating algorithm we provide its probabilistic interpretation and its generalization for the long-term forecasting. For the special basic case of Vovk’s algorithm we provide two its modifications for the long-term forecasting. The first one is theoretically close to an optimal algorithm and is based on replication of independent copies. It provides the time-independent regret bound with respect to the best expert in the pool. The second one is not optimal but is more practical (explicitly models dependencies in observations) and has $O(\sqrtT)$ regret bound, where $T$ is the length of the game.