Adaptive Approach Algorithm Based On Polynomial Model To Predict Chaotic Time Series

It is known to all that the law of motion in reality is non-linear. Non-linear phenomena exist both in natural world and human society. Among many non-linear phenomena, chaotic time series attracts people wildly. For example, climate change, electricity supply, and economic index can all be seen as chaotic time series. Therefore, an accurate prediction will undoubtedly have great practical significance and value. But because of some characteristics like initial condition sensitiveness and inherent randomness of chaotic time series, the traditional time series prediction methods are not good enough. Hence, using chaos theory to predict is an important question in the time series prediction. This paper, according to the general knowledge of chaos theory, centers around chaotic time series prediction and function approaches theory, explores some adaptive and prospective calculations, and finally proposes and realizes several algorithm which are available for chaotic time series. This paper, first, introduces the definition of chaos theory and the corresponding indexes which describes the chaos system; second, analyzes the theory of three prediction methods: full-area prediction, local prediction, and adaptive prediction; third, proposes a chaotic time series prediction algorithm based on polynomial and RLS algorithm; fourth, proposes a chaotic time series prediction based on polynomial and LMS algorithmIn order to meet the requirement of speed and accuracy in the adaptive prediction, the main work of the paper is to propose two kinds of algorithms based on polynomial and adaptive algorithms.(1) On the basis of Bernstein polynomial and RLS algorithm to make an adaptive prediction, this paper puts forward three kinds of orthogonal polynomials: Chebyshev polynomial, Hermite polynomial and Laguerre polynomial, which are combined with the RLS algorithm to make anadaptive prediction.The experimental results show that, compared to the original algorithm with the same accuracy, the proposed algorithm is much faster.(2) Because of the computational complexity of the LMS algorithm is lower than RLS algorithm, this paper proposes some algorithm based on LMS algorithm, which combined with Legender polynomial, Chebyshev polynomial, Hermite polynomial, Laguerre polynomial and Bernstein polynomial respectively, to make the adaptive prediction. The experimental results show that the proposed algorithm, compared with the RLS algorithm with nearly the same accuracy, decreases the computational time by 50%, the algorithm is significantly improved.