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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 processes are an important class of stochastic processes that can be modeled as a complete power law (PPL) process. Since the scale index δ of PPL process can completely characterize its second-order statistical properties, the estimation of δ is the key to completing the mathematical model. Considering the approximate band-pass characteristics of wavelet filters and the properties of stationary wavelet transform, a new method of fractal index estimation for stationary FD processes based on wavelet analysis is proposed. Firstly, the stationary wavelet transform of the process is used to obtain the sub-processes at each scale, and then the unbiased estimates of the variance of these sub-processes are given. Finally, the functional relationship between variance and scale is established and linearly regression is performed on the variance and scale in the logarithmic sense , To complete the estimate. Computer simulation shows that the method has higher accuracy.