Chaotic Time Series Multi-Step Ahead Prediction

Student: Denikin Viacheslav

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2021

Predicting chaotic time series is one of the most pressing problems of modern data analysis, and multi-step ahead prediction is especially difficult. One of the reasons for this is that we rarely see a purely chaotic processes, and most of the time there is a part of randomness in the observations. The Fokker-Planck equation is oftenly used to describe the evolution of the density distribution of a random variable. In this paper, a model is constructed that generalizes the regular Fokker-Planck equation to the cases of non-Markov processes, non-additive entropy, ambiguity of the system, nonlinearity of time, and the presence of the observer effect. Also, a detailed analysis of its most common special cases has been done. Ways for the numerical construction of solutions based on the methods of Newton and Kantorovich for two particular cases are presented and the corresponding numerical results are obtained.

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