Fractal Analysis Of The Intertrade Durations In China's Stock Market

In this thesis, we use kinds of fractal analysis methods, including monofractal and multi-fractal, to describe the intertrade durations'characteristics in many areas, based on the data of the 20 stocks in Shanghai Stock Exchange, in 79 trading days from January 4,2010 to April 30,2010. After analyzed the basic statistical characteristics of the intertrade durations, we found that, the intertrade durations performance long-range memory, intraday pattern and non-stability, as the other financial ultra-high frequency data. These basic descriptions of the statistical characteristics inform us that fractal analysis methods could be used to describe the long-range memory and some other local features of the intertrade duration much better and more accurately.In the using of the Detrended Fluctuation Analysis method, one of the monofractal analysis methods, to analysis of the data of intertrade duration we found that, there exists clear long-range memory in the series of intertrade duration, and the existence of such long-range memory is a common phenomenon, it dependent with these factors, such as the industry sector which the stocks in, total market capitalization and the total average trading intensity. In addition, the original data of the intertrade duration were carried out in three different approaches:removing the intraday pattern, shuffling and Fourier-phase randomization, the results of these different process upon the original data were compared, we can see that, the existence of the intraday pattern barely affects the long-range memory of intertrade duration, the long-range memory comes from the internal relevant of the series, because the series after shuffled doesn't performances any significant long-rang memory. At the same times, we discover that, the curves of the fluctuation functions of the intertrade durations constitutes with two lines with different slopes, these suggest that in different time scales the long-range memory of the intertrade durations appear differently, so we conclude that it's not reasonable and accuracy to quantify the long-range memory in different time scales of the whole series. Therefore, we use three different multi-fractal analyses method to describe the multi-fractal feathers of the intertrade durations.Multi-fractal analysis of the empirical results show that in the data of intertrade duration there exists clear multi-fractal feathers, in different time scales, the series show significantly different characteristics. In order to find the cause of the appearance of these multi-fractal feathers, we processed the original data using different approaches, and compare the analysis result, we found that the multi-fractal feathers of the intertrade durations mainly come from the inherent correlation within sequence and the non-normality of the sequence, and the latter has a greater impact on the existence of the multi-fractal characteristics.Through the monofractal and multi-fractal analysis of the intertrade duration, we have a better understanding of the intrinsic relationship between different trades in China's stock market. It's very useful for us to understand and explain the real activity of exchange in stock market.