融合子带方差和FD变换的长记忆过程仿真

Simulation and Check of LMP by Sub-band Variance and FD Transform

根据长记忆过程小波变换的频带分割及其去相关性,提出了“子带方差”的概念,并给出了在长记忆条件下的估算公式。在此基础上,构造了一种具有扩展记忆功能的FD变换,该变换可以将一个无记忆的、独立同分布的随机序列转化为具有指定长记忆特性的随机序列,由此实现对长记忆过程的仿真。对仿真序列进行模型比较和参数估计证实,基于子带方差的FD变换可以有效地扩展和控制随机序列的记忆性。

Due to the decorrelation and frequency-band partition of DWT for long memory process （LMP）, a physical quantity called sub-band variance was proposed, and its approximating expression was given under the fractionally differenced （FD） parameters or spectral density is specified. Moreover, a special diagonal matrix and a related transformwere constructed, which can transform an IID stochastic sequence into a sample of FD process. Simulation samples were compared with the theoretical model, and their statistical properties were checked in two ways. The results validate that the sequence memory can be effectively extended and controlled by the transform based on sub-band variance.