Analysis Of Stock Market Fluctuation Based On Wavelet Analysis

Stock fluctuations are a normal feature of stock market. Moderate fluctuations help to improve market liquidity and increase the degree of market activity. Violent and frequent fluctuations distort the market price mechanism, lead to loss of stock market efficiency and thus weaken the market function to optimize resource allocation. China's stock market is an emerging market. Market fluctuations are accompanied by high risk and low efficiency. Stock market fluctuations affect the risks and benefits of investors. Thus, fluctuations of the market have been of concern to investors and financial researchers. Many scholars study the stock market in China, mainly in three areas: first, phase division of China's stock market, second, trend analysis of stock market data, and third, analysis of the factors affecting the stock market. This paper, based on the fluctuations of Shanghai Composite Index, analyzes the fluctuations of the stock market. The Shanghai Composite Index as a focus for researchers has the obvious non-stability. Wavelet analysis as a rapid mathematical field is a new signal processing method and has been widely used in signal analysis, image processing, etc. As a time series, financial data have the same characteristics with the signal we usually analyze. Therefore, in recent years, wavelet analysis in finance is also increasingly becoming a major analytical tool. Wavelet analysis can decompose signal wavelet to the frequency channels of different scales. Because of the more singleness of the decomposed signals than the original one in frequency components, and due to the smoothing of signals by wavelet decomposition, after some non-stationary time series were decomposed by wavelet, they can be regarded as approximate stationary time series to deal with. Transformed wavelet will not lose the original sequence information when reconstructed, and can carry on multi-resolution analysis of different scales. Because of "adaptive" and the "zoom" feature of the wavelet function, it can effectively deal with non-stationary signal. This paper adopts the Daubechies-5 wavelet and Symlet-2 wavelet with effective denoising and without distortion if reconstructed to give the Shanghai index three-layer decomposition, reconstruction, noise reduction and multi-resolution analysis. This paper also tries to find the singular points in the volatility of Shanghai Composite Index and to analyze its causes so as to make stage classification of the volatility characteristics more accurate. Finally, the smoothed curve based on the wave theory can predict the trend for the stock market.