Based On The Multifractal Spectrum Of High-frequency Data Empirical Research

According to the fractal theory and multifractal principle, we get a new calculation method to real stock data for calculatingαand f(α); then we choose 5 minutes high-frequency index time-series of the ShangHai A-share market, 5 minutes high-frequency price time-series of 5 individual stocks, 15 and 5 minutes high-frequency price time-series data of TaiShan Petroleum stocks , use this new method and make their multifractal spectrums by using the software MATLAB7.1, we get the main indexes of their own multifractal spectrums and their multifractal spectrums, through analyzing their own multifractal spectrums and their indexes, we get three main conclusions:1. Through analyzing 5 minutes high-frequency index time-series of the ShangHai A-share market, we prove that the stocks market has the character of the multifractal, and make the conclusion that the stock market is indeed a nonlinear system;2. To 5 individual stocks ,we analyze their multifractal spectrums, through the large number of experimental results, we get a new conclusion that we can forecast the next movements of the stock by observing their multifractal spectrums' shape and index in the recent time;3. To 15 and 5 minutes high-frequency price time-series data of TaiShan Petroleum stocks compared with its price, we make the useful conclusion that if the higher frequency of the data, the more information that the stocks contain, the more easily to forecast future trends of the stocks, this conclusion can solve the selection question of the high-frequency time-series data better.