Abstract: Alipschitz exponentα, which reflects the singlaritynature of stock data, is obtainedwithwavelet transform and muti-scale analysis by regarding stock day profit ratio as a one-dimentional time signal.αin this paper is negative, showing that the singularity is more singular than non-continuum. This proves that the variation of stock prices is fractal. At the same time, it is pointed out that when scalesis very big, wavelet transform and multi-scale analysis can remove the up-and-down of stock market data caused by accidental factors and give prominence to primary factors and macroscopic sudden change points. This is important in predicting the variation trend of stock prices frommacroscopic aspect.