Прогнозирование хаотических временных рядов на много шагов вперёд
In this paper, using the example of the Lorentz series, we consider several new strategies for predicting many steps ahead. The use of generalized z-vectors, composed of inconsistent observations, made it possible, within the framework of prediction approaches based on clustering, to construct for each point for which it is necessary to obtain a forecast, a sufficiently large set of possible forecast values. The analysis of these sets was carried out in two aspects: first, the determination of the possibility of obtaining a single predicted value for such a set; secondly, the construction of a single predicted value in cases where it is possible. The concept of unpredictable points made it possible to formulate a new problem of predicting many steps ahead, which assumes that the algorithm has the ability to distinguish between predictable and unpredictable points and to make a forecast in predictable ones. It was found that with increasing number of steps for which it is necessary to obtain a predicted value, the number of unpredictable points increases, while the error in the predicted points does not exceed a certain threshold value. The approaches proposed in this work to solving the problem of multistep predictionin this formulation made it possible to obtain predicted values at some points beyond the prediction horizon.