基于小波分析的非平稳FD过程分形指数估计

提出了一种非平稳FD过程分形指数估计的新方法。首先对过程进行平稳小波变换以获得各个尺度下的子过程。随后给出这些子过程方差的无偏估计;最后建立方差与尺度的函数关系,并在对数意义下对方差和尺度作线性回归,从而完成估计。计算机仿真表明该方法具有较高精度。

Estimation of the Fractional Exponent of Non-stationary Fractional Differencing Process Based on Wavelet Analysis

A new estimating method to the fractional exponent of Non-Stationary Fractional Differencing Process is presented. Firstly, stationary wavelet transform is applied to get the branch processes corresponding to all scalls. Secondly, the unbiased estimation of the variances of the branch processes is worked out. Finally, the relation between the variances and the scalls is formulated and carrying out linear regression between the variances and the scalls is carried out in the logarithm sense to finish the estimation. The result of the simulation indicates that the method is comparatively accurate.