Development of adaptive combined models for predicting time series based on similarity identification

Adaptive combined models of hybrid and selective types for prediction of time series on the basis of a program set of adaptive polynomial models of various orders were offered. Selection in these models is carried out according to B-, R-, P-criteria with automatic formation of the basic set of models based on the adaptive D-criterion. It was found that these models had the maximum accuracy in the case of short-term and medium-term prediction of time series.Adaptive combined selective prediction models based on the R- and B-criteria of selection with identification of similarities in the retrospection of time series by the nearest neighbor method was proposed. An adaptive combined hybrid model of prediction with identification of similarities in the retrospection of time series was constructed. It was found that these models had the highest accuracy in the case of medium-term prediction of time series.Estimation of the prediction efficiency of various combined models depending on the level of persistency of time series was made. It has been found that in the case of short-term prediction for the prediction period τ≤2, the adaptive combined hybrid prediction model is the most accurate. Selective models with various selection criteria are effective in predicting persistent time series with the Hurst index H>0.75 for the prediction period τ>2. In the case of prediction of time series with the Hurst index for the prediction period τ>2, the adaptive combined hybrid and selective models with identification of similarities in the retrospection of the time series are more precise.