【作者】 聂淑媛；

【导师】 李文林；

【作者基本信息】 西北大学 ， 科学技术史， 2012， 博士

【摘要】 在当前信息化时代,数据的处理和分析至关重要,时间序列分析作为一套独具特色、自成体系的数据分析和处理方法被广泛应用,逐渐引起科学家和社会学家的高度重视。对于这样备受关注的学科,尽管国内外的教材较为丰富,有关历史发展研究的文献却不多见,而且多是一些概括性、粗略性的介绍,零散地分布于各种专著和论文之中,因此,系统地研究时间序列分析的历史演化过程具有重要的理论价值和现实意义。本文在已有研究基础上,以“为什么数学”作为方法论指导,主要运用了以下研究方法：以原始文献为依据,内史与外史相结合；全面进行纵向和横向比较,注重不同时期关键人物和核心工作之间的传承关系；注重不同学科间的交叉和融合。主要研究成果为：1.首次以时间序列分析的起源、基本概念对学科发展的推动、以及时间序列分析两大主体方法的初步发展为主线,系统地梳理了时间序列分析早期发展的历史脉络,为时间序列分析学科史的研究提供了一条清晰的线索。2.对于时间序列分析的起源问题,众说纷纭、观点不一,本文通过对原始文献的剖析,首次提出了平稳时间序列产生的背景正是Graunt的关键性创新思想——统计比率对于时间和空间的稳定性,并根据Graunt各种现代时问序列思想的萌芽,以及对Pearson的学术影响,肯定了Graunt在时间序列分析上的先驱地位。3.探讨了时间序列分析基本概念——差分、指数与滑动平均等从金融算术到政治算术,到科学算术,最后进入到现代化数学领域的发展历程,展现了这些最初只是金融家进行贸易猜测和掩盖真相的技术工具,如何被统计学家逐步借鉴、运用到实证研究中,并推动着现代时间序列分析形成的发展历程。4.概括了时间序列分析两大方法——频域分析和时域分析的早期发展,详细考察了Schuster在Fourier级数理论的基础上,创建周期图方法的背景、过程及应用。对周期图方法缺陷的讨论和修订,不仅引导着频域分析方法的提升,而且刺激了时域分析方法的初步发展,文章细致分析了时域分析中平稳时间序列三大模型——线性自回归AR模型、移动平均MA模型和自回归移动平均ARM A模型的创建过程及其相互之间的传承关系,并特别强调,Wold对于离散平稳时间序列的综合研究,不仅概括了AR模型和MA模型,更结合了Khinchin、Kolmogorov研究平稳随机过程的概率理论,以及Schuster的周期图方法。最后,以Wold分解定理的基础、诞生、发展及影响为主线,梳理了时间序列分解的发展历程。5.分析了经济学、统计学思想与时间序列分析学科的交叉、融合：以价格平衡问题、稳定和扰动概念、经济学家和统计学家对贸易循环的共同关注以及Lexis的实证研究等典型问题为例,阐述了经济学对时间序列分析的影响；以回归与相关引发“时间相关问题”,促使回归概念发展到自回归概念为主线,阐述了统计学对时间序列分析的影响。更多还原

【Abstract】 In present information age, it is essential to process and analyse data. Due to its unique, self-contained methods for data analysis and processing, time series analysis has been widely applied to many areas and is drawing scientist’s great attention. In spite of the rich teaching material, research literature on its historical development for such a frontier subject is still wanting, and most of historical introduction in existence are briefly and concisely scattering in various monographs and papers. Systematic studies on the historical evolution of time series analysis are therefore necessary and of both theoretical and practical significance.Based on the existing research work on the considered field and regarding "why mathematics?" as its methodological guide, the thesis takes the following main research approaches:deep investigation into the original literature, combination of the internal and external historical view; comparitive studies comprehensively from the vertical and horizontal perspective, in particular, in the inheritance relationship between the key figures in different periods and their core theory; emphasizing the interaction and integration between different disciplines. The main results are as follows:l.The historical context of the early development of time series analysis is systematically sorted for the first time by major consideration of the origin of the basic concepts which impulse the growth of the subject and the initial development of its two principal methods. The thesis therefore provides a clear clue for the study of the discipline history of time series analysis.2. Facing diverse opinions for the origin of time series analysis, the thesis first clearly points out by analyzing the original literature that the background of arising of stationary time series was right the concept "stable statistical ratios over time and space", which was Graunt’s key innovative idea. Combined with the exposition of Graunt’s all germinating ideas of modern time series and his academic influence on Pearson, it establishes firmly the historical place of Graunt as a pioneer of time series analysis.3. The development process of the basic concepts including the difference, the index number and the moving average is explored, from monetary arithmetic to political arithmetic, then to scientific arithmetic, and finally into the modern mathematical areas. It displays how the statisticians gradually applied these technical tools, which were initially used to speculate and cover up the truth by financiers, into empirical investigation and laid theoretical foundation for the modern time series analysis.4. The early development of the two principle methods——the frequency domain method and the time domain method of time series is summarized. The background, evolution and application of periodogram method created by Schuster on bases of the theory of Fourier series are discussed in detail. The improvment of periodogram method not only led to the advancement of frequency domain method but also stimulated the early development of time domain method. The thesis analyses carefully the establishing process and the inheritance relationship of three models of stationary time series (auto regression model, moving average model and auto regression moving average model), with emphasis on that Wold’s comprehensive study in the discrete stationary time series not only integrated the AR model and MA model, but also combined Khinchin and Kolmogorov’s probability theory which had been used to study the stationary random process as well as Schuster’s periodogram method. At last, the development of time series decomposition is described by observing mainly the birth, progress and influence of Wold decomposition theorem.5. The interaction and integration of economics and statistics with time series analysis are investigated. The impact of economics on time series analysis is described by taking the typical cases such as:the price equilibrium problem, the concept of stationary and disturbance, economists and statisticians’common concern about the trade cycle, Lexis’ empirical investigation; The main line of elaborating the impact of statistics on time series analysis is the fact that regression and correlation led to time-correlation problem and promoted the concept evolution from regression to autoregression.更多还原