基于分数阶差分模型的记忆性扩展方法

由小波变换的去相关性,给出了分数阶差分(FD)模型下小波变换系数协方差矩阵的一种近似计算方法,并由此构造了一种具有扩展记忆功能的矩阵变换,它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记忆特性的随机过程样本,由此实现对随机序列记忆性的扩展。通过对实际构造序列进行模型比较和参数估计证实,基于FD模型的记忆性扩展方法在统计意义上是正确的、有效的。

Approach for extending sequence memory based on fractionally differenced model

Based on the decorrelation and frequency-band partitions of DWT for long memory process (LMP), a ap-proximating covariance matrix was given and a related transform was constructed, which could transform an IID stochas-tic vector into a sample realization of fractionally differenced (FD) process. To carry out this transform, a physical quan-tity called sub-band variance was proposed and computed under the FD parameters specified. At last, construction sam-ples were compared with theoretical model, and their statistical properties were checked in two ways. Computing results validate that the algorithm presented is feasible, rational and effective in a statistical sense.