基于小波分析的PPL过程尺度指数估计

Estimation of Scale Exponent of PPL Process Based on Wavelet Analysis

长记忆随机过程是一类重要的随机过程,可以将其建摸为完全幂规律(PPL)过程。鉴于PPL过程的尺度指数δ能完全刻画其二阶统计特性,从而使得δ的估计成为完成数学模型的关键。考虑到小波滤波器的近似带通特性以及平稳小波变换的性质,文章提出了一种基于小波分析的平稳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。

Long memory stochastic process can be modeled as Perfect Power Law Process is an important branch of the stochastic process family.The Scale Exponent δ is crucial to finish the mathematical model, in which δ completely portrays the second order statistical property of the Perfect Power Law Process. Considering the property of the Stationary Wavelet Transform and the fact that a wavelet filter is an approximate band-pass filter, a new method to estimate the δ is presented, the steps are, firstly, applying stationary wavelet transform to get the branch processes corresponding to all scales, secondly, working out the unbiased estimation on the variances of the branch processes, finally, formulating the relation between the variances and the scales and carrying out linear regression between the variances and the scales in the logarithm sense to finish the estimation. The result of the simulation indicates that the method is comparatively accurate.