Time Series Forecasting Using Nonlinear Dynamic Methods and Identification of Deterministic Chaos

摘要

The study is devoted to the application of nonlinear dynamic methods to explore and model chaotic processes. The criteria of deterministic chaos and the general stages of modeling time series are presented in the work. It is proposed to improve the forecast accuracy by the identification of the chaotic component of the time process using deterministic nonlinear dynamic systems with chaotic solutions in terms of small number of available observations and one process implementation. Decomposition in the system of chaotic processes described by the logistic map is used as a model of chaotic signal. Moreover the parameter of the logistic map and the state of the system of each previous step are known inaccurately and are estimated using the unscented Kalman filter (UKF). Divergence process due to rounding estimations of the parameters of the systems is analyzed in the research.