Study And Application Of Chaotic Time Series Prediction

Chaotic time series widely exist in production and daily life. Theexterior feature of this kind of series is similar to purely random motion,with random and disordered character like random noise. It isunpredictable in long term. However, the intrinsic nonlinear dynamicsstructure makes it possible for short-term prediction. Traditionalforecasting methods can not obtain satisfactory result. It has become aresearch hotspot to solve the prediction problem of this kind of serieswith Chaos Theory.This paper focused on the chaotic time series prediction, and made astudy on each step of the forecasting process. The main contentsinclude following.1) Chaos Theory basic definitions and concepts;2)The phase space reconstruction of chaotic time series;3) The chaoticnature discrimination of time series;4) Chaotic time series prediction.The main research results are as follows.(1) The paper analysed current solving methods of two keyparameters of phase space reconstruction, delay time and embeddingdimension. Improved G-P algorithm and improved C-C algorithm wereproposed to achieve faster and more accurate solution of reconstructionparameters.(2) Three types of chaotic time series prediction methods wereintroduced—global method, local method and self-adaptive method.Local method was chosen as the prediction method due to its lowercomputation complexity, faster, higher precision and strongeradaptability.(3) A new neighboring phase point selection method based onevolution-tracking was proposed to avoid including pseudo neighboring points, which is a common problem of current selection methods.(4) In addition, a method based on the HQ criterion was adopted todetermine the number of neighboring phase points. It overcomes theshortcoming of traditional methods which choose the number bysubjective experience or repeated experiments.(5) Finally, a local prediction algorithm of chaotic time series viasupport vector machine with Sigmoid kernel was presented in this paper.A software was completed according to the new algorithm. As two casestudies, Lorenz chaotic system and short-term power load prediction wereexamined in details and results show that the algorithm predicts moreaccurately than traditional algorithm and has a good overall performanceand application prospect.