Xie-Zhongjie编著的《时间序列分析实例研究》是一本有关时间序列分析应用于实际的实证分析研究的专著。全书分为两大部分：第一部分简要介绍了时间序列分析的基础理论和方法，这些内容是读懂本书各案例研究所必备的基本知识；第二部分是案例研究。从中读者可看出时间序列分析是如何广泛地应用于实际并成为解决各种问题的核心工具。书中的案例涉及到当年中国科学家从自己的观测记录中是如何发现天王星的光环的；滤波理论如何应用于中国东海和黄海的重力勘探；谱分析如何判别先天性愚型儿童的脑电特征、多元谱的K-L信息量如何应用于优秀飞行员的生理特征的检测；潜周期分析如何发现离体脑垂体仍有内分泌的节律周期；预测理论如何应用于气象的建模和预报，等等许多非常有趣而真实的研究案例。这些研究成果使作者获得了中国国家自然科学奖和国内外的多项奖项。

《时间序列分析实例研究》是一本有关时间序列分析应用于实际的实证分析研究的专著。全书分为两大部分：第一部分简要介绍了时间序列分析的基础理论和方法。这些内容是读懂本书各案例研究所必备的基本知识；第二部分是案例研究。从中读者可看出时间序列分析是如何广泛地应用于实际并成为解决各种问题的核心工具。书中的案例涉及到当年中国科学家从自己的观测记录中是如何发现天王星的光环的，滤波理论如何应用于中国东海和黄海的重力勘探，谱分析如何判别先天性愚型儿童的脑电特征、多元谱的K-L信息量如何应用于优秀飞行员的生理特征的检测，潜周期分析如何发现离体脑垂体仍有内分泌的节律周期。预测理论如何应用于气象的建模和预报，等等许多非常有趣而真实的研究案例。这些研究成果使作者Xie-Zhongjie获得了中国国家自然科学奖和国内外的多项奖项。

读者通过本书的学习不仅可学到时间序列分析的基本理论和方法，更重要的是本书介绍了”如何将一个实际问题转化成数学问题”，然后运用数学和统计学的理论和方法加以解决，这包括最后还原到实际，用实验数据加以检验的完整过程。

《时间序列分析实例研究》可作为应用时间序列分析领域的大学生和研究生教学参考书或补充教材，也是应用统计工作者和相关学科的科技人员、工程师很有价值的参考资料。

Preface

PART ONE

An Introduction to the Theory and Methods of Time Series Analysis

Chapter 1.Theory of Stationary Time Series

I.I 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 He and

the functional space L2(dF)

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 processes

Chapter 2.ARMA Model and Model Fitting

2.1 ARMA model and the Wold decomposition

2.2 Orthogonal basis in Hilbert Space H

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 problem

Chapter 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 AR,MA models

3.2 The linear filtering of time series

3.3 Spectral analysis of time series

3.3.1 Theory and methods of hidden periodicities analysis

3.3.2 Theory and methods of spectral density estimations

PART 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 thc 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)

I.Introduction

2.Spectral analysis of VEP records for dull and normal children

31 Statistical analysis for detection of characteristics

4.Physiological interpretation

Appendix III

Case IV.Statistical Analysis of VEP and AI by the Principal Component Analysis of Time Series in Frequency Domain

1.Introduction

2.Principal component analysis in frequency domain and its application in AI analysis

3.Practical checking

4.Discussion

Appendix IV

Case V.Periodicity Analysis of LH Release in Isolated Pituitary Gland by Hidden Frequency Analysis

1.Introduction

2.Statistical analysis of LH release

3.Practical rhythm analysis of LH release

4.Discussion

Case VI.Statistical Detection of Uranian Ring Signals from the Light Curve of Photoelectric Observation

1.Introduction

2.Statistical detection of weak ring signals from the noise background

3.Discussion

Case VII.On the Forecasting of Freight Transportation by a New Model Fitting Procedure of Time Series

1.Introduction

2.A new model fitting procedure for freight transportation prediction

3.Forecasting for freight transportation of practical data

4.Dicussion

Appendix VII

 A.1 On the X-11 processing procedure

 A.2 Simple exponential smoothing predictor

 A.3 Program for fitting a spline function

Case VIII.The Water Flow Prediction in Xiang River

1.Introduction

2.Constructing a prediction formula based on the hidden periodicities by the quantile method

3.Comparison and discussion

Appendix VIII

 A.1 Quantile method for detecting the hidden periodicities

 A.2 RMA forecasting method

Case IX.Miscellaneous Cases Study

IX.1 Long term weather forecasting by seasonal ARIMA model

 IX.I.1 Some relevant knowledge

 (1) Seasonal ARIMA model

 (2) M.L.E.and M.S.S.E.under the normal distribution

 (3) Powell's algorithm for seeking the extreme value of a convex function

 (4) Roots identification of a polynomial by Jury's method

IX.1.2 Modelling and forecasting for the temperature in Shanghai

IX.2 Outlier analysis and interpolation of missing data in a measuring system

 IX.2.1 Basic knowledge on outlier analysis

 IX.2.2 Interpolation for missing data for AR(p) model

 IX.2.3 Practical application for a range measuring system

Bibliography

Subject Index