Using of intermediate point predictions to predict chaotic time series with many steps forward

The proposed work (within the clustering prediction paradigm) presents an approach to predicting chaotic time series by many steps at least for those points for which such a forecast is possible. This is used to forecast the forecast values at intermediate points of the forecasting interval and proposes algorithms for estimating the reliability of these forecast values. The above tasks require the use of clustering algorithms based on the apparatus of graph theory to find characteristic sequences (motives) in a known part of the predicted series and their use in obtaining the forecast. When predicting many steps forward, the predicted values at intermediate points are obtained using the algorithm. Namely, the use of the concept of inconsistent observation patterns proposed by the authors in the formation of sample vectors to be clustered at the stage of motive identification allows one to obtain many (albeit correlated) forecasts for one point; analysis of many forecasts allows you to drop obviously erroneous forecasts. In addition, three estimates for the projected points were constructed: the top estimate is the estimate obtained by applying motives to all observed points; lower estimate - an estimate obtained by applying motives only to those points on which you can rely; we will know these points; approximation of the lower estimate - the estimate obtained by applying motives only to those points on which you can rely, while the support points will be selected according to the value of their invariant measure. The following can be indicated as the main planned research results: (1) establishing the nature of the dependence of the number of unpredictable points and the average forecast error for points for which a forecast is possible, as a function of the length of the forecast interval; (2) algorithms for assessing the reliability of the obtained forecast values at intermediate points of the forecasting interval and evaluating their impact on the quality of forecasting; (3) the construction of a system of algorithms that allows predicting chaotictime series many steps forward.