Research On High-frequency Data In Stock Markets With Wavelet Analysis

Wavelet analysis is a novel object and method, which includes abundant mathematical contents. With extensive applied potential, wavelet has been a powerful research instrument in many applied and engineering subjects. This paper puts wavelet into use on analysis and research of financial high-frequency data, which creates new field to use wavelet analysis. The main work and innovations of the dissertation include:1,Wavelet analysis is used to take intraday periodicity apart from interday volatility. The periodicity is divided on different scales. With scale enlarged, calendar effect is becoming smoother and smoother. The characteristic of high Skewness and Kurtosis is independently present.2,On basis of wavelet variance, the author defines wavelet Skewness and wavelet Kurtosis. Moreover, the author uses them in analyzing cross-correlation of high-frequency time series in stock markets. The result is that cross-correlation of yield and volatility is different from different scales in Shanghai Stock Market and Shenzhen Stock Market. With scale enlarged, cross-correlation is strengthening.3,The paper connects long-memory process with wavelet, emphasizes on such theories as discrete wavelet transform of long-memory process, simulation with wavelet and Least Squares Estimation of Fractionally Differenced process. Then the paper analyses long-memory of high-frequency data in stock markets and puts them into different scales.4,The paper clears away the noise of high-frequency time series by using wavelet analysis. There are different results with various rules and wavelet functions. But in all, the result with wavelets is better than traditional denoising methods.In the end, the author brings out sum-up and expectation about the paper and points out the research direction in the future.