Chaotic time series have been involved in many fields of production and life, so their prediction has a very important practical value. However, due to the characteristics of chaotic time series, such as internal randomness, nonlinearity, and long-term unpredictability, most prediction methods cannot achieve high-precision intermediate or long-term predictions. Thus, an intermediate and long-term prediction (ILTP) method for n-dimensional chaotic time series is proposed to solve this problem. Initially, the order of the model is determined by optimizing the preprocessing and constructing the joint calculation strategy, so that the observation sequence can be decomposed and reorganized accurately. Furthermore, the RBF neural network is introduced to construct a multi-step prediction model of future sequences, with a feedback recursion mechanism. Compared with the existing prediction methods, the error of the ILTP method can be reduced by 1–6 orders of magnitude, and the prediction step can be increased by 10–20 steps. The ILTP method can provide reference technology for the application of time series prediction with chaotic characteristics.

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To improve the estimation accuracy of chaotic time series and reduce the computational complexity, a high-precision adaptive blind estimation method is proposed. By introducing the pre-treatment method, the adaptive identification model is established, and the linear estimation equation is derived. Through the organic combination of the model and the least square mechanism, the complexity of the model is limited. When changing the type and length of the sequence, the parameters can be changed adaptively, so as to construct the corresponding trajectory equation and realize the blind estimation of chaotic time series. The analysis and experimental results show that the estimation accuracy of this method can reach 10 -16 order of magnitude.

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