The Wavelet And Fractal Analysis On The Stockmarket’s High Frequency Data

In1970, Fama provided Efficient Market Hypothesis (EMH), from then on. this hypothesis has become the fundamental theory in the modern finance, and based on this hypothesis, the modern finance mansion had been bulit. However, since1970s, there are lots of anomalies in finance market which EMH cannot explain.Thus, from1980s, in order to strongly explain the finance market, there are many scholars explored from lots of different aspects to find the new theory and new model to fit the actual world. The most influential theory is Fractal Theory which famous from1990s. Fractal Theory put forward that the fluctuation of finance market is a nonlinear dynamics system, which has the characteristics of long-range correlation and the trend of circulation. The application of Fractal Theory in finance market becomes the Fractal Market Hypothesis. This theory does not need the serious hypotheses like the EMH, and it focus on the market liquidity and the influence of investment horizon to investors, thus, it is more approaching to the reality to give the description of the investor behaviour and the model of the market price movement.In recent years, with the development of calculation’s technology and methodology, the research of finance data has focus on the time record with more and more accurate data, that is, high frequency data. High frequency data can precisely and detailed reflect the characteristics of the market microstructure, thus, it has the value of research on expositing the market price, exploring the measurement of financial risk, promoting the reasonable pricing of assets, and promoting the formation of derivative.In2005, the appearance of Shanghai and Shenzhen300index in our country offset the vacancy in our country’s stock market which does not have the index to reflect the overall trends in the crossing market. This index support the investors to measure their investment securities return, besides, based on this index, there are many index fund products which regard Shanghai and Shenzhen300index as the tracking object in the market, which provide the decentralized investment channels for the medium and small investors and at the same time expand the number of institutional investors in the market. Therefore, it is more significant to do the research on the characteristics of Shanghai and Shenzhen300index.At present, there is little research on the Shanghai and Shenzhen300index. This paper is based on the Fractal Theory, and use the wavelet analysis to systematically and comprehensively analyze the fractal feature of days of yields and income volatility of the Shanghai and Shenzhen300index, and introduce the Empirical Mode Decomposition (EMD) to de-noising in the high frequency yield/closing price at the first time. In this research, high frequency days of yields array and income volatility array are not only have the characteristics in single fractal, but also in the multi fractal, and in terms of de-noising effects, the decomposition algorithm of empirical mode is better than wavelet analysis.