The Early Development Of Time Series Analysis

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.