时间序列分析：预测与控制（英文版·第3版）——图灵原版数学·统计学系列

    本书自1970年初版以来，不断修订再版，以其经典性和权威性成为有关时间序列分析领域书籍的典范。书中涉及时间序列随机(统计)模型的建立及许多重要的应用领域的使用，包括预测，模型的描述、估计、识别和诊断，动态关系的传递函数的识别、拟合及检验，干预事件影响的建模和过程控制等专题。本书叙述简明，强调实际技术，配有大量实例。
　　本书可作为统计和相关专业高年级本科生或研究生教材，也可以作为统计专业技术人员的参考书。

时间序列分析是一门实用性很强、蓬勃发展的数据分析技术，现在广泛地应用于工业质量控制、生物基因工程和金融数据分析等诸多领域。而这一切的发展不能不提到G.E.P.BOX和G.M.JE-NKINS以及二人合著的最早于1970年出版的《时间序列分析――预测与控制》。由于二位对时间序列数据分析的巨大贡献，大家将本书提出的ARIMA模型命名为BOX-JENKINS模型。
在这本时间序列分析经典之作中，几位统计大家用极其通俗的语言，运用大量的实例，深入浅出而又形象地阐明时间序列分析的精髓，使读者免去过多繁杂的数学公式推导证明，而很快掌握实践的技巧，体会其中直观而深刻的思想。相信每一位研读此书的读者都会获益匪浅。

George E.P.Box 国际级统计学家。曾于1960年创立威斯康星大学统计系并任该系主任，现为该校名誉教授。BOX发表过200多篇论文，出版过很多重要著作，其中本书和STATISTICE FOR
EXPERIMENTERS为其代表作。
Gwilym M.Jenkins 已故国际级统计学家。曾于1966年创立了英国兰开斯特大学系统工程系。JENKINS与BOX合作的成果对时间序列分析方法的研究和应用产生了巨大的推动作用。
Gregory C.Reinsel 已故国际级统计学家。1995-1997年任威斯康星大学统计系系主任。因在统计领域的突出贡献而被推举为美国统计协会会士。

1　INTRODUCTION　1
1.1　Four Important Practical Problems　2
1.1.1　Forecasting Time Series　2
1.1.2　Estimation of Transfer Functions　3
1.1.3　Analysis of Effects of Unusual Intervention Events To a System　4
1.1.4　Discrete Control Systems　5
1.2　Stochastic and Deterministic Dynamic Mathematical Models　7
1.2.1　Stationary and Nonstationary Stochastic Models for Forecasting and Control　7
1.2.2　Transfer Function Models　12
1.2.3　Models for Discrete Control Systems　14
1.3　Basic Ideas in Model Building　16
1.3.1　Parsimony　16
1.3.2　Iterative Stages in the Selection of a Model　16

Part I　Stochastic Models and Their Forecasting　19

2　AUTOCORRELATION FUNCTION AND SPECTRUM OF STATIONARY PROCESSES　21
2.1　Autocorrelation Properties of Stationary Models　21
2.1.1　Time Series and Stochastic Processes　21
2.1.2　Stationary Stochastic Processes　23
2.1.3　Positive Definiteness and the Autocovariance Matrix　26
2.1.4　Autocovariance and Autocorrelation Functions　29
2.1.5　Estimation of Autocovariance and Autocorrelation Functions　30
2.1.6　Standard Error of Autocorrelation Estimates　32
2.2　Spectral Properties of Stationary Models　35
2.2.1　Periodogram of a Time Series　35
2.2.2　Analysis of Variance　36
2.2.3　Spectrum and Spectral Density Function　37
2.2.4　Simple Examples of Autocorrelation and Spectral Density Functions　41
2.2.5　Advantages and Disadvantages of the Autocorrelation and Spectral Density Functions　43
A2.1　Link Between the Sample Spectrum and Autocovariance Function Estimate　44

3　LINEAR STATIONARY MODELS　46
3.1　General Linear Process　46
3.1.1　Two Equivalent Forms for the Linear Process　46
3.1.2　Autocovariance Generating Function of a Linear Process　49
3.1.3　Stationarity and Invertibility Conditions for a Linear Process　50
3.1.4　Autoregressive and Moving Average Processes　52
3.2　Autoregressive Processes　54
3.2.1　Stationarity Conditions for Autoregressive Processes　54
3.2.2　Autocorrelation Function and Spectrum of Autoregressiue Processes　55　
3.2.3　First-Order Autoregressive (Markov) Process　58
3.2.4　Second-Order Autoregressive Process　60
3.2.5　Partial Autocorrelation Function　64
3.2.6　Estimation of the Partial Autocorrelation Function　67
3.2.7　Standard Errors of Partial Autocorrelation Estimates　68
3.3　Moving Average Processes　69
3.3.1　Invertibility Conditions for Moving Average Processes　69
3.3.2　Autocorrelation Function and Spectrum of Moving Average Processes　70
3.3.3　First-Order Moving Average Process　72
3.3.4　Second-Order Moving Average Process　73
3.3.5　Duality Between Autoregressive and Moving Average Processes　75
3.4　Mixed Autoregressive-Moving Average Processes　77
3.4.1　Stationarity and Invertibility Properties　77
3.4.2　Autocorrelation Function and Spectrum of Mixed Processes　78
3.4.3　First-Order Autoregressive-First-Order Moving Average Process　80
3.4.4　Summary　83
A3.1　Autocovariances Autocovariance Generating Function and Stationarity Conditions for a General Linear Process　85
A3.2　Recursive Method for Calculating Estimates of Autoregressive Parameters　87

4　LINEAR NONSTATIONARY MODELS　89
4.1　Autoregressive Integrated Moving Average Processes　89
4.1.1　Nonstationary First-Order Autoregressive Process　89
4.1.2　General Model for a Nonstationary Process Exhibiting Homogeneity　92
4.1.3　General Form of the Autoregressive Integrated Moving Average Process　96
4.2　Three Explicit Forms for the Autoregressive Integrated Moving Average Model　99
4.2.1　Difference Equation Form of the Model　99
4.2.2　Random Shock Form of the Model　I00
4.2.3　Inverted Form of the Model　106
4.3　Integrated Moving Average Processes　109
4.3.1　Integrated Moving Average Process of Order (0,1,1)　110
4.3.2　Integrated Moving Average Process of Order (0,2,2)　114
4.3.3　General Integrated Moving Average Process of Order (0,d,q)　118
A4.1　Linear Difference Equations　120
A4.2　IMA(0,1,1) Process With Deterministic Drift　125
A4.3　ARIMA Processes With Added Noise　126
A4.3.1　Sum of Two Independent Moving Average Processes　126
A4.3.2　Effect of Added Noise on the General Model　127
A4.3.3　Example for an IMA(O,1,1) Process with Added White Noise　128
A4.3.4　Relation Between the IMA(O,1,1) Process and a Random Walk　129
A4.3.5　Autocovariance Function of the General Model with Added Correlated Noise　129

5　FORECASTING　131
5.1　Minimum Mean Square Error Forecasts and Their Properties　131
5.1.1　Derivation of the Minimum Mean Square Error Forecasts　133
5.1.2　Three Basic Forms for the Forecast　135
5.2　Calculating and Updating Forecasts　139
5.2.1　Convenient Format for the Forecasts　139
5.2.2　Calculation of the ψ Weights　139
5.2.3　Use of the ψ Weights in Updating the Forecasts　141
5.2.4　Calculation of the Probability Limits of the Forecasts at Any Lead Time　142
5.3　Forecast Function and Forecast Weights　145
5.3.1　Eventual Forecast Function Determined by the Autoregressive Operator　146
5.3.2　Role of the Mooing Average Operator in Fixing the Initial Values　147
5.3.3　Lead l Forecast Weights　148
5.4　Examples of Forecast Functions and Their Updating　151
5.4.1　Forecasting an IMA(O,1,1) Process　151
5.4.2　Forecasting an IMA(O,2,2) Process　154
5.4.3　Forecasting a General IMA(O,d,q) Process　156
5.4.4　Forecasting Autoregressive Processes　157
5.4.5　Forecasting a (1,O,1) Process　160
5.4.6　Forecasting a (1,1,1) Process　162
5.5　Use of State Space Model Formulation for Exact Forecasting　163
5.5.1　State Space Model Representation for the ARIMA Process　163
5.5.2　Kalman Filtering Relations for Use in Prediction　164
5.6　Summary　166
A5.1　Correlations Between Forecast Errors　169
A5.1.1　Autocorrelation Function of Forecast Errors at Different Origins　169
A5.1.2　Correlation Between Forecast Errors at the Same Origin with Different Lead Times　170
A5.2　Forecast Weights for Any Lead Time　172
A5.3　Forecasting in Terms of the General Integrated Form　174
A5.3.1　General Method of Obtaining the Integrated Form　174
A5.3.2　Updating the General Integrated Form　176
A5.3.3　Comparison with the Discounted Least Squares Method　176

Part II　Stochastic Model Building　181

6　MODELDENTIFICATION　183
6.l　Objectives of Identification　183
6.1.1　Stages in the Identification Procedure　184
6.2　Identification Techniques　184
6.2.1　Use of the Autocorrelation and Partial Autocorrelation Functions in Identification　184
6.2.2　Standard Errors for Estimated Autocorrelations and Partial Autocorrelations　188
6.2.3　Identification of Some Actual Time Series　188
6.2.4　Some Additional Model Identification Tools　197
6.3　Initial Estimates for the Parameters　202
6.3.1　Uniqueness of Estimates Obtained from the Autocovariance Function　202
6.3.2　Initial Estimates for Moving Average Processes　202
6.3.3　Initial Estimates for Autoregressive Processes　204
6.3.4　Initial Estimates for Mixed Autoregressive-Moving Average Processes　206
6.3.5　Choice Between Stationary and Nonstationary Models in Doubtful Cases　207
6.3.6　More Formal Tests for Unit Roots in ARIMA Models　208
6.3.7　Initial Estimate of Residual Variance　211
6.3.8　Approximate Standard Error for 　212
6.4　Model Multiplicity　214
6.4.1　Multiplicity of Autoregressive-Moving Average Models　214
6.4.2　Multiple Moment Solutions for Moving Average Parameters　216
6.4.3　Use of the Backward Process to Determine Starting Values　218
A6.1　Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process　218
A6.2　General Method for Obtaining Initial Estimates of the Parameters of a Mixed Autoregressive-Moving Average Process　220

7　MODELESTIMATION　224
7.l　Study of the Likelihood and Sum of

本书涉及时间序列随机(统计)模型的建立及其在重要应用领域的使用。这包括预测，模型的估计、鉴别和检验，动态关系的传递函数建模，干预事件影响的建模以及过程控制等专题。在《时间序列分析：预测与控制》第一版面世的同时，有关上述专题的研究掀起了巨大的热潮。因此，在这一版中，我们在保留有关时间序列分析的一些基本原理的同时，也融入了由众多作者提供的大量的新思想、新的修正和改进意见。 在本书上一版的写作期间，Gwilym Jenkins正以非凡的勇气与一场慢性衰竭病症作斗争。在本次的修订中，作为对他的纪念，我们保持了原书的总体结构，仅对原文进行适当的修改和删节。具体来说，第7章关于ARIMA模型的估..