【作者】 王松伟；

【导师】 文成林；

【作者基本信息】 河南大学 ， 应用数学， 2006， 硕士

【摘要】 时间序列分析是统计学的分支之一,它的研究对象是离散有序数列的变化特征和变化趋势。长时间来,时间序列分析在经济、金融、管理、气象、水文、海洋、地球物理、生物、医学、机械、电子等很多领域都得到了广泛的应用,因此对于时间序列分析方法的探索始终是研究的热点。传统方法主要是时域法和频域法,但一般不具备多尺度的分析功能以及不能同时拥有良好的时频特性。在自然界和工程实践中,许多现象或过程都具有多尺度特征或多尺度效应。同时,人们对现象或过程的观察及测量往往也是在不同尺度上进行的,因此,用多尺度系统理论来描述、分析这些现象或过程是十分自然的,它能够很好地表现这些现象或过程的本质特征。此外,在解决许多实际问题时,多尺度分析这种时频方法具有思路清晰、简洁、计算复杂度低等优点。将多尺度的思想应用到时间序列分析中,就是所谓的多尺度时间序列分析。本文中,我们在多尺度框架内,对时间序列分析中的几个基本问题和方法,即二阶矩分析、时间序列模型参数的极大似然估计以及时间序列的实时动态预报,进行了发展和研究,丰富了传统的时间序列分析方法。具体工作如下:1.时间序列的多尺度方差反映了时间序列在不同尺度上的波动性,是在多尺度框架下从二阶统计量中提取信息的基础。本文研究了多尺度方差的基本属性,给出了多尺度方差的估计方法及估计值置信区间的求法。并且作为一个应用,将多尺度方差应用到时间序列谱密度函数的估计上。2.利用小波变换的解相关属性,分别发展了基于离散小波变换和离散小波包变换的多尺度极大似然估计方法,有效地降低了传统似然函数估计中存在的计算量大的问题,同时这种估计算法也是满足一定精度要求的。3.针对经济、金融等环境中存在有大量周期性的非平稳时间序列,将卡尔曼滤波方法和多尺度分析方法相结合,提出了具有实时性、递归性和多尺度分析能力的扩展小波-卡尔曼滤波混合估计与预报方法。它考虑了一些非经济因素的影响,可实现对时间序列周期内的实时跟踪估计和动态多步预报。更多还原

【Abstract】 As one of the branches of statistics, time series analysis focuses on the variation characters and trend of discrete ordered data series mainly. For a long time, time series analysis has been applying in many fields successfully, such as economics, finance, management, chronometer, aerography, oceanography, physical geography, biology, iatrology, mechanics, electronic engineering etc. So the exploration of the theories and methods of time series has always been a hot research topic. The main methods of time series analysis consist of time domain methods and frequency domain methods. However, without the perfect time-frequency quality, most of these methods usually can not do some multi-scale analysis.In nature and engineering practices, many phenomena or processes have the multi-scale characters or multi-scale effects. While people often observe or measure phenomena and processes at different scales. So it is natural to describe and analysis these phenomena and processes according to multi-scale system theory which can show the essence of these phenomena and processes appropriately. Besides, as a time-frequency method, multi-scale analysis can solve many practical problems in a conceit way with the low computation complexity.Applying the multi-scale analysis into time series analysis is the so-called multi-scale time series analysis. In the multi-scale framework, this thesis has developed and researched several basic problems and methods of time series analysis, that is, the analysis of second-order moment, maximum likelihood estimation of process parameters and the real-time dynamic forecasting of time series, which enrich the traditional analysis methods of time series. The main contributions of this thesis are as follows:1. The multi-scale variance reflects the variability of time series at scales, and provides a base upon which information about two-order moment can be abstracted in a multi-scale framework. In this thesis, the basic property of the更多还原