時間序列分析實例研究

內(nèi)容概要

本書是一本有關時間序列分析應用于實際的實證分析研究的專著。全書分為兩大部分：第一部分簡要介紹了時間序列分析的基礎理論和方法。這些內(nèi)容是讀懂本書各案例研究所必備的基本知識；第二部分是案例研究。從中讀者可看出時間序列分析是如何廣泛地應用于實際并成為解決各種問題的核心工具。書中的案例涉及到當年中國科學家從自己的觀測記錄中是如何發(fā)現(xiàn)天王星的光環(huán)的，濾波理論如何應用于中國東海和黃海的重力勘探，譜分析如何判別先天性愚型兒童的腦電特征、多元譜的K-L信息量如何應用于優(yōu)秀飛行員的生理特征的檢測，潛周期分析如何發(fā)現(xiàn)離體腦垂體仍有內(nèi)分泌的節(jié)律周期。預測理論如何應用于氣象的建模和預報，等等許多非常有趣而真實的研究案例。這些研究成果使作者獲得了中國國家自然科學獎和國內(nèi)外的多項獎項。    讀者通過本書的學習不僅可學到時間序列分析的基本理論和方法．更重要的是本書介紹了”如何將一個實際問題轉(zhuǎn)化成數(shù)學問題”，然后運用數(shù)學和統(tǒng)計學的理論和方法加以解決，這包括最后還原到實際，用實驗數(shù)據(jù)加以檢驗的完整過程。    本書可作為應用時間序列分析領域的大學生和研究生教學參考書或補充教材，也是應用統(tǒng)計工作者和相關學科的科技人員、工程師很有價值的參考資料。

作者簡介

北京大學教授 從事時間序列、序貫分析研究

書籍目錄

PrefacePART ONEAn Introduction to the Theory and Methods of Time Series AnalysisChapter 1.Theory of Stationary Time Series  1.1 The definition of stationary stochastic processes　1.2 The spectral representation of covariance function　1.3 The Hilbert space of second order processes　1.4 Stochastic integral and the isomorphic relationship between H~ and the functional space L2(dFe)    1.4.1 Orthogonal stochastic measure    1.4.2 Stochastic integral and the representation of stationary processes    1.4.3.Karhunen theorem　1.5 Strong law of large numbers for stationary series　1.6 Sampling theorem for stochastic stationary processesChapter 2.ARMA Model and Model Fitting　2.1 ARMA model and the Wold decomposition　2.2 Orthogonal basis in Hilbert space Hf　2.3 The covariance function of ARMA model and Yule-Walker equation　2.4 Model fitting under the criterion of one-step ahead prediction error　2.5 M.E.model fitting for observed data     2.5.1 M.E.model fitting with sample covariance     2.5.2 Order selection problemChapter 3.Prediction, Filtering and Spectral Analysis of Time Series　3.1 Prediction of time series     3.1.1 The prediction formula for AR models     3.1.2 The prediction formula for ARMA models　3.2 The linear filtering of time series　a.a Spectral analysis of time series     3.3.1 Theory and methods of hidden periodicities analysis     3.3.2 Theory and methods of spectral density estimationsPART TWO Case Studies in Time Series Analysis　Case I.Digital Processing of a Dynamic Marine Gravity Meter　　1.Problem statement and working diagram of a dynamic marine gravity meter　　2.The first test for solving the problem　　3.Design a new digital filter under Min-Max criterion　　4.The frequency rectification by filtering　　5.Practical checking in the prospecting field of the East Sea of China　Case II.Digital Filters Design by Maximum Entropy Modelling　　1.Problem statement　　2.Design the filter by maximum entropy modelling　　3.A practical filter design　Case III.The Spectral Analysis of the Visual Evoked Potentials of Normal and Congenital Dull Children (Down's disease)　　1.Introduction　　2.Spectral analysis of VEP records for dull and normal children　　3.Statistical analysis for detection of characteristics　　4.Physiological interpretation　Appendix III　Case IV.Statistical Analysis of VEP and AI by the Principal Component Analyis of Time Serise in Frequency Domain   Case V.Periodicity Analysis of LH Release in Isolated Pituitary Gland by Hidden Frequency Analysis  Case VI.Statistical Detection of Uranian Ring Signnals from the Light Curve of Photoelectric Observation  Case VII.On the Forecasting of Freight Transportation by a New Model Fitting Procedure of Time Series  Case VIII.The Water Flow Prediction in Xiang River  Case IX.Miscellaneous Cases StudyBibliography Subject Index

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