Wavelet Analysis And Its Application On China’s Stock Market

The stock market is characterized by high-return, high-risk. Since the stock market was established, many scholars have tried to solve how to analyze the stock market. There are a lot of conventional methods, such as the moving average method, the grey system theory, the neural network forecasting method. They play a very important role on the analysis of the stock market. The data of the stock market is large, variable and noised. Especially in china, violent and frequent fluctuations are normal. So it’s difficult to carry on analysis for the stock market using the above methods.On the basis of Fourier analysis method, wavelet analysis was introduced in1984. Because of the adaptability and the ability of localizing both time and frequency domain, wavelet analysis is suitable for analyzing the non-stationary data of the stock market. In this paper, we introduce the four applications of the wavelet transformation in financial data analysis, and conduct many empirical studies to the daily closing prices which come from the Shanghai Stock Exchange and the Shenzhen Stock Exchange after2005. In particular, we do the following studies.(1) We pre-treat the data of the Shanghai composite index, thenthe wavelet toolbox of MATLAB software is used for the wavelet decomposition of the data. It’s well known that the fluctuations of stock market are caused by the noise. So we try to analyze the high frequency parts at each level which are obtained from the wavelet decomposition. We can identify the stock market’s singularities from the previous analysis. Then we study the singularities further.(2) Utilizing the fractal character of the wavelet multi-resolution analysis, we can remove the noise of the stock market data, and make the trend more obvious. Through the wavelet decomposition and reconstruction to the daily closing price of the Shenzheng index, we can get the de-noised stock chart. Using the periodical analysis method, we try to find the regularity of stock market movements.(3) As we all know, moving average method is one of the major linear analysis methods. But because of its time delaying, there are some errors in the analytical results by using the moving average method. Through the study, we find that the time delaying can be effectively solved by using the low frequency data obtained from wavelet decomposition to replace the short-term moving average line in the moving average method. In this thesis, we will make an empirical research on the daily closing prices of China Merchants Bank by using the advanced method.(4) As two main important indexes of China’s stock market, the study of the relevance between the Shanghai Composite Index and Shenzhen Component Index is very popular in recent years. In this thesis, we will discuss the variance and correlation coefficients between the two main indexes. Based on wavelet analysis, the wavelet variances of the Shanghai and Shenzhen stock, and wavelet correlation coefficients between the two indexes are calculated. Then we obtain the relevance of the two stock markets by analyzing the wavelet correlation coefficients.