目 录
中文摘要
ABSTRACT
第一章 绪 论............................................................................................................1
§1.1 研究背景....................................................................................................1
§1.2 国内外研究现状........................................................................................2
§1.3 本文研究的内容........................................................................................9
第二章 小波相关理论............................................................................................10
§2.1 离散小波变换的定性描述 ....................................................................10
§2.2 小波滤波器..............................................................................................15
§2.3 尺度滤波器..............................................................................................17
§2.4 塔式算法..................................................................................................18
§2.5 小波频谱和小波相关系数 ....................................................................22
第三章 长记忆过程定义和检验方法....................................................................23
§3.1 长记忆过程定义 ....................................................................................23
§3.2 长记忆过程一般模型 ............................................................................23
§3.2.1 分形高斯噪声 ................................................................................23
§3.2.2 完全幂律过程 ................................................................................25
§3.2.3 分形差分过程 ................................................................................25
§3.3 长记忆检验方法......................................................................................27
§3.3.1 标准对数周期图法 ........................................................................27
§3.3.2 修正对数周期图发 ........................................................................27
§3.3.3 小波分析方法..................................................................................28
第四章 长记忆过程建模........................................................................................30
§4.1 概念和定义 ............................................................................................30
§4.1.1 严平稳过程 ....................................................................................30
§4.1.2 宽平稳过程 ....................................................................................30
§4.1.3 白噪声过程 ....................................................................................31
§4.2 自回归模型..............................................................................................31
§4.2.1 自回归模型描述...............................................................................31
§4.2.2 自相关函数 ....................................................................................32
§4.2.3 序列自相关系数的作用 ................................................................33
§4.3 移动平均模型..........................................................................................34