Online Aggregation of Conformal Forecasting Systems

Abstract—

The problem of online probabilistic time series forecasting is considered. Probabilistic forecasts are obtained as a result of the application of conformal forecasting systems. The conformal forecasting system is defined on the basis of point forecasts of the regression algorithm. The corresponding probability distribution function is used to assess the degree of reliability of the algorithm’s predictions. The paper considers the case when at each moment of time several competing methods (experts) present their forecasts in the form of distribution functions. These distributions are constructed online from point predictions using the conformal prediction method. The probabilistic forecasts of experts are combined using an aggregating algorithm into one probabilistic forecast at each stage of the forecasting process, while expert forecasts can be used at a discount. A technology has been developed for constructing predictive expert algorithms and aggregation of their probabilistic forecasts on the example of the problem of forecasting the hourly load of an electric network depending on the temperature forecast. The results of numerical experiments on real data are presented; a comparative analysis of the method of conformal predictions and the method of Gaussian mixtures is carried out.