Diffusion Entropy Analysis And Probability Flux Analysis Based On EMD

The study of scale invariance has been payed more and more attention to for complex systems. The methods currently used to determine the scaling exponent of a complex dynamic time series are based on numerical evaluation of variance. That means all this methods can be safely applied to the case where the variances are finite but fail to determine the scaling exponent when the variances are infinite or don't exit. Most time series of the complex dynamic system have infinite variances or don't have variances. In this paper we study a statistic method based on the Shannon entropy of the diffusion process generated by a time series and a statistic method based on the cumulative probabilities. Both methods can well determine the scaling exponent of the series with infinite variances or without variances. In this paper, first we will improve the binning algorithm of the diffusion entropy analysis. And then we will discuss the distinction between diffusion entropy analysis and probability flux analysis applied to Guass model and Levy model. We then try to combine empirical mode decompose and the two methods separately. After the combination we apply the two methods to Guass model and Levy model. We study the differences between before and after the combination. We use the conclusions to study the scaling properties and statistic properties of the stocks index datas.