时间序列分析|图灵原版数学·统计学系列|George E.P.Box等|人民邮电出版社

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时间序列分析

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原书名：Time Series Analysis: Forecasting and Control	原出版社：Prentice Hall/Pearson
作者： George E.P.Box等	出版社：人民邮电出版社
译者：	丛书名：图灵原版数学·统计学系列
出版日期：2006-7-28	上架日期：2006-7-31 9:40:00
ISBN：7115137722	页数：598 版次：1-1
开本：16开	装帧：平装
读者对象：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。

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| 大封面 | 封底 | 前言 | 内容简介 | 序言 | 目录 | 作者简介 | 译者简介 | 作者序 | 译者序 |

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内容简介
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。
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.Jenkins以及二人合著的《时间序列分析预测和控制》。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，使读者免去过多数学公式推导证明的繁杂，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。

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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 Squares Functions　224
7.1.1　Likelihood Function　224
7.1.2　Conditional Likelihood for an ARIMA Process　226
7.1.3　Choice of Starting Values for Conditional Calculation　227
7.1.4　Unconditional Likelihood; Sum of Squares Function; Least Squares Estimates　228
7.1.5　General Procedure for Calculating the Unconditional Sum of Squares　233
7.1.6　Graphical Study of the Sum of Squares Function　238
7.1.7　Description of“Well-Behaved” Estimation Situations; Confidence Regions　241
7.2　Nonlinear Estimation　248
7.2.1　General Method of Approach　248
7.2.2　Numerical Estimates of the Derivatives　249
7.2.3　Direct Evaluation of the Derivatives　251
7.2.4　General Least Squares Algorithm for the Conditional Model　252
7.2.5　Summary of Models Fitted to Series A to F　255
7.2.6　Large-Sample Information Matrices and Covariance Estimates　256
7.3　Some Estimation Results for Specific Models　259
7.3.1　Autoregressive Processes　260
7.3.2　Moving Average Processes　262
7.3.3　Mixed Processes　262
7.3.4　Separation of Linear and Nonlinear Components in Estimation　263
7.3.5　Parameter Redundancy　264
7.4　Estimation Using Bayes' Theorem　267
7.4.1　Bayes' Theorem　267
7.4.2　Bayesian Estimation of Parameters　269
7.4.3　Autoregressive Processes　270
7.4.4　Moving Average Processes　272
7.4.5　Mixed processes　274
7.5　Likelihood Function Based on The State Space Model　275
A7.1　Review of Normal Distribution Theory　279
A7.1.1　Partitioning of a Positive-Definite Quadratic Form　279
A7.1.2　Two Useful Integrals　280
A7.1.3　Normal Distribution　281
A7.1.4　Student's t-Distribution　283
A7.2　Review of Linear Least Squares Theory　286
A7.2.1　Normal Equations　286
A7.2.2　Estimation of Residual Variance　287
A7.2.3　Covariance Matrix of Estimates　288
A7.2.4　Confidence Regions　288
A7.2.5　Correlated Errors　288
A7.3　Exact Likelihood Function for Moving Average and Mixed Processes　289
A7.4　Exact Likelihood Function for an Autoregressive Process　296
A7.5　Examples of the Effect of Parameter Estimation Errors on Probability Limits for Forecasts　304
A7.6　Special Note on Estimation of Moving Average Parameters　307

8　MODEL DIAGNOSTIC CHECKING　308
8.1　Checking the Stochastic Model　308
8.1.1　General Philosophy　308
8.1.2　Overfitting　309
8.2　Diagnostic Checks Applied to Residuals　312
8.2.1　Autocorrelation Check　312
8.2.2　Portmanteau Lack-of-Fit Test　314
8.2.3　Model Inadequacy Arising from Changes in Parameter Values　317
8.2.4　Score Tests for Model Checking　318
8.2.5　Cumulative Periodogram Check　321
8.3　Use of Residuals to Modify the Model　324
8.3.1　Nature of the Correlations in the Residuals When an Incorrect Model Is Used　324
8.3.2　Use of Residuals to Modify the Model　325

9　SEASONALMODELS　327
9.1　Parsimonious Models for Seasonal Time Series　327
9.1.1　Fitting versus Forecasting　328
9.1.2　Seasonal Models Involving Adaptive Sines and Cosines　329
9.1.3　General Multiplicative Seasonal Model　330
9.2　Representation of the Airline Data by a Multiplicative (0,1,1) ~ (0,1,1)12 Seasonal Model　333
9.2.1　Multiplicative (0,l,l) ~ (0,l,1)12 Model　333
9.2.2　Forecasting　334
9.2.3　Identification　341
9.2.4　Estimation　344
9.2.5　Diagnostic Checking　349
9.3　Some Aspects of More General Seasonal Models　351
9.3.1　Multiplicative and Nonmultiplicative Models　351
9.3.2　Identification　353
9.3.3　Estimation　355
9.3.4　Eventual Forecast Functions for Various Seasonal Models　355
9.3.5　Choice of Transformation　358
9.4　Structural Component Models and Deterministic Seasonal Components　359
9.4.1　Deterministic Seasonal and Trend Components and Common Factors　360
9.4.2　Models with Regression Terms and Time Series Error Terms　361
A9.1　Autocovariances for Some Seasonal Models　366

Part III　Transfer Function Model Building　371

10　TRANSFER FUNCTION MODELS　373
10.1　Linear Transfer Function Models　373
10.1.1　Discrete Transfer Function　374
10.1.2　Continuous Dynamic Models Represented by Differential Equations　376
10.2　Discrete Dynamic Models Represented by Difference Equations　381
10.2.1　General Form of the Difference Equation　381
10.2.2　Nature of the Transfer Function　383
10.2.3　First- and Second-Order Discrete Transfer Function Models　384
10.2.4　Recursive Computation of Output for Any Input　390
10.2.5　Transfer Function Models with Added Noise　392
10.3　Relation Between Discrete and Continuous Models　392
10.3.1　Response to a Pulsed Input　393
10.3.2　Relationships for First-and Second-Order Coincident Systems　395
10.3.3　Approximating General Continuous Models by Discrete Models　398
A10.1　Continuous Models With Pulsed Inputs　399
A10.2　Nonlinear Transfer Functions and Linearization　404

11　IDENTIFICATION FITTING AND CHECKING OF TRANSFER FUNCTION MODELS　407
ll.1　Cross Correlation Function　408
11.1.1　Properties of the Cross Covariance and Cross Correlation Functions　408
11.1.2　Estimation of the Cross Covariance and Cross Correlation Functions　411
11.1.3　Approximate Standard Errors of Cross Correlation Estimates　413
11.2　Identification of Transfer Function Models　415
11.2.1　Identification of Transfer Function Models by Prewhitening the Input　417
11.2.2　Example of the Identification of a Transfer Function Model　419
11.2.3　Identification of the Noise Model　422
11.2.4　Some General Considerations in Identifying Transfer Function Models　424
11.3　Fitting and Checking Transfer Function Models　426
11.3.1　Conditional Sum of Squares Function　426
11.3.2　Nonlinear Estimation　429
11.3.3　Use of Residuals for Diagnostic Checking　431
11.3.4　Specific Checks Applied to the Residuals　432
11.4　Some Examples of Fitting and Checking Transfer Function Models　435
11.4.1　Fitting and Checking of the Gas Furnace Model　435
11.4.2　Simulated Example with Two Inputs　441
11.5　Forecasting Using Leading Indicators　444
11.5.1　Minimum Mean Square Error Forecast　444
11.5.2　Forecast of C02 Output from Gas Furnace　448
11.5.3　Forecast of Nonstationary Sales Data Using a Leading Indicator　451
11.6　Some Aspects of the Design of Experiments to Estimate Transfer Functions　453
A11.1　Use of Cross Spectral Analysis for Transfer Function Model Identification　455
All.I.1　Identification of Single Input Transfer Function Models　455
All.l.2　Identification of Multiple Input Transfer Function Models　456
AI1.2　Choice of Input to Provide Optimal Parameter Estimates　457
All.2.1　Design of Optimal Inputs for a Simple System　457
All.2.2　Numerical Example　460

12　INTERVENTION ANALYSIS MODELS AND OUTLIER DETECTION　462
12.1　Intervention Analysis Methods　462
12.1.1　Models for Intervention Analysis　462
12.1.2　Example of Intervention Analysis　465
12.1.3　Nature of the MLE for a Simple Level Change Parameter Model　466
12.2　Outlier Analysis for Time Series　469
12.2.1　Models for Additive and Innovational Outliers　469
12.2.2　Estir m ation of Outlier Effect for Known Timing of the Outlier　470
12.2.3　Iterative Procedure for Outlier Detection　471
12.2.4　Examples of Analysis of Outliers　473
12.3　Estimation for ARMA Models With Missing Values　474

Part IV　Design of Discrete Control Schemes　481

13　ASPECTS OF PROCESS CONTROL　483
13.1　Process Monitoring and Process Adjustment　484
13.1.1　Process Monitoring　484
13.1.2　Process Adjustment　487
13.2　Process Adjustment Using Feedback Control~488
13.2.1　Feedback Adjustment Chart　489
13.2.2　Modeling the Feedback Loop　492
13.2.3　Simple Models for Disturbances and Dynamics　493
13.2.4　General Minimum Mean Square Error Feedback Control Schemes　497
13.2.5　Manual Adjustment for Discrete Proportional-Integral Schemes　499
13.2.6　Complementary Roles of Monitoring and Adjustment　503
13.3　Excessive Adjustment Sometimes Required by MMSE Control　505
13.3.1　Constrained Control　506
13.4　Minimum Cost Control With Fixed Costs of Adjustment And Monitoring　508
13.4.1　Bounded Adjustment Scheme for Fixed Adjustment Cost　508
13.4.2　Indirect Approach for Obtaining a Bounded Adjustment Scheme　510
13.4.3　Inclusion of the Cost of Monitoring　511
13.5　Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes　514
A13.1　Feedback Control Schemes Where the Adjustment Variance Is Restricted　516
A13.1.1　Derivation of Optimal Adjustment　517
A13.2　Choice of the Sampling Interval　526
A13.2.1　Illustration of the Effect of Reducing Sampling Frequency　526
A13.2.2　Sampling an IMA(O,I,I) Process　526

Part V　Charts and Tables　531

COLLECTION OF TABLES AND CHARTS　533
COLLECTION OF TIME SERIES USED FOR EXAMPLES IN THE TEXT AND IN EXERCISES　540
REFERENCES　556

Part VI　EXERCISES AND PROBLEMS　569

INDEX　589

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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。

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