时间序列分析：预测与控制 英文版

　　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。 CONTENTS 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

　　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。