Like Chaotic Characteristics Of The Stock Index Signal Denoising

Chaos is the phenomenon of pseudo-random uncertainty in deterministic nonlinear dynamical systems. It reveals the common characteristics of the nonlinear subjects:the unity of uncertainty and randomness, the unity of order and disorder, the unity of quantitative and qualitative change. Wang Qing, Chen Ting, Li Feng in "irrational and chaotic-like sequence in the application of image encryption"[1] proposed the concept of Chaos-like characteristics and and discussed using time series analysis in order to prove the Chaos-like characteristics of irrational numbers.In the first part of this article, the last century the U.S. Dow Jones stock index series and 20 years of the Shanghai Stock Composite Index series is simulated using relevant time series analysis. Specific methods include power spectral analysis, principal component analysis, phase-space reconstruction, calculating the maximum Lyapunov parameter and correlation dimension method. The numerical analysis proved that stock index signals have the Chaos-like characteristics.Subsequently, it discussed the chaotic signal denoising. The main research focus local geometric projection-one of the more effective method-is the selection of the neighborhood. It reveals the relationship between correlation dimension and the signal to noise ratio of noisy chaotic series. It treated correlation dimension as the radius standards of local projection for denoising. The stock time series of a certain time frame is analyzed to test the denoising effect. Prediction of chaotic sequences is compared with the forecast before denoising to prove the feasibility and necessity of denoising from chaotic signal.