Multifractal description of stock price index fluctuation using a quadratic function fitting

In order to obtain a quantitative multifractal characterization of the stock price index, the multifractal spectrum of Shanghai stock price index time series in 2005 was investigated and the multifractal spectrum was fitted using a quadratic function. A sliding window of 240 frequency data in 5 trading days was used to investigate the stock price index fluctuation. The multifractal parameters and coefficients in each window were obtained by fitting the local multifractal spectrum using a quadratic function. It is found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by the multifractal parameters and the quadratic function coefficients. This has led to a better understanding of complex stock markets.