Abstract:This paper introduces a new volatility measure and constructs its model based on multifractal volatility method． Taking 5-minute high frequency data of the Shanghai Composite Index as an example，and applying the out-of-sample rolling time window forecasting combined with Model Confidence Set which is proved superior to SPA test，this paper compares the empirical performance of the new model and those of the GAＲCH-type and Ｒealized volatility (RV) models． The empirical results show that the forecasting accuracy of the multifractal volatility measure model in the short term as well as in the long term are better than the GARCH-type and RV models． Moreover，the forecasting models in the long term perform better than those in the short term．The performance in most loss function of the new method based on multifractal volatility measure is superior to other forecasting models．

Abstract:The market dynamics exhibits extremely turbulent behaviors around the financial crisis point．The correct locating of financial crisis point is the key step of distinguishing the multifractal properties of stock market both before and after financial crisis．Comparing with other methods，the wavelet transform modulus maxima ( WTMM) method has its advantages in detecting the outliers and indentifying the multifractal properties in financial markets．The time points of financial crisis are identified though the maxima lines of DJI and TPX indices，which are estimated by WTMMThe multifractal analysis of DJI is further performed around the time points where the outliers are detected．From our analysis，the WTMM is found to be capable of not only on correctly locating the time point of financial crisis，but also characterizing the evolution of the multifractal features both before and after financial crisis．Our empirical results also verify the Fractal Market Hypothesis (FMH) on the causes of market crash and provide a new idea for financial risk management．

Abstract:Multifractal is a powerful tool to describe the complexity of fluctuations in financial markets, and the multifractal spectrum of financial price time series is a concrete and complete description of its complex characteristics. Take the multifractal spectrum of high frequency price time series of Shanghai Stock Exchange Composite index as example, a new market risk measure based on two main parameters of multifractal spectrum is constructed, which may make up for the shortcomings of traditional risk measur...

Abstract:Many recent researches with empirical data have demonstrated that financial data have multifractal prop2erties , but seldomwith Chinese financial data. In this paper we study the Shanghai Stock Exchange Composite Index(SSECI) and find that return volatility correlations are power2laws with a non-unique scaling exponent . The result isquite similar to other researcher’s findings. Since multifractal models for financial market can provide us much in2formation about volatility , we suppose the associated research between multifractal and risk management would besignificative.