时间序列分析 预测与控制 英文版 第3版【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

时间序列分析 预测与控制 英文版 第3版PDF格式电子书版下载

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1 INTRODUCTION1

1.1 Four Important Practical Problems2

1.1.1 Forecasting Time Series2

1.1.2 Estimation of Transfer Functions3

1.1.3 Analysis of Effects of Unusual Intervention Events To a System4

1.1.4 Discrete Control Systems5

1.2 Stochastic and Deterministic Dynamic Mathematical Models7

1.2.1 Stationary and Nonstationary Stochastic Models for Forecasting and Control7

1.2.2 Transfer Function Models12

1.2.3 Models for Discrete Control Systems14

1.3 Basic Ideas in Model Building16

1.3.1 Parsimony16

1.3.2 Iterative Stages in the Selection of a Model16

Part 1 Stochastic Models and Their Forecasting19

2 AUTOCORRELATION FUNCTION AND SPECTRUM OF STATIONARY PROCESSES21

2.1 Autocorrelation Properties of Stationary Models21

2.1.1 Time Series and Stochastic Processes21

2.1.2 Stationary Stochastic Processes23

2.1.3 Positive Definiteness and the Autocovariance Matrix26

2.1.4 Autocovariance and Autocorrelation Functions29

2.1.5 Estimation of Autocovariance and Autocorrelation Functions30

2.1.6 Standard Error of Autocorrelation Estimates32

2.2 Spectral Properties of Stationary Models35

2.2.1 Periodogram of a Time Series35

2.2.2 Analysis of Variance36

2.2.3 Spectrum and Spectral Density Function37

2.2.4 Simple Examples of Autocorrelation and Spectral Density Functions41

2.2.5 Advantages and Disadvantages of the Autocorrelation and Spectral Density Functions43

A2.1 Link Between the Sample Spectrum and Autocovariance Function Estimate44

3 LINEAR STATIONARY MODELS46

3.1 General Linear Process46

3.1.1 Two Equivalent Forms for the Linear Process46

3.1.2 Autocovariance Generating Function of a Linear Process49

3.1.3 Stationarity and Invertibility Conditions for a Linear Process50

3.1.4 Autoregressive and Moving Average Processes52

3.2 Autoregressive Processes54

3.2.1 Stationarity Conditions for Autoregressive Processes54

3.2.2 Autocorrelation Function and Spectrum of Autoregressive Processes55

3.2.3 First-Order Autoregressive(Markov)Process58

3.2.4 Second-Order Autoregressive Process60

3.2.5 Partial Autocorrelation Function64

3.2.6 Estimation of the Partial Autocorrelation Function67

3.2.7 Standard Errors ofPartial Autocorrelation Estimates68

3.3 Moving Average Processes69

3.3.1 Invertibility Conditions for Moving Average Processes69

3.3.2 Autocorrelation Function and Spectrum of Moving Average Processes70

3.3.3 First-Order Moving Average Process72

3.3.4 Second-Order Moving Average Process73

3.3.5 Duality Between Autoregressive and Moving Average Processes75

3.4 Mixed Autoregressive-Moving Average Processes77

3.4.1 Stationarity and Invertibility Properties77

3.4.2 Autocorrelation Function and Spectrum of Mixed Processes78

3.4.3 First-Order Autoregressive-First-Order Moving Average Process80

3.4.4 Summary83

A3.1 Autocovariances,Autocovariance Generating Function,and Stationarity Conditions for a General Linear Process85

A3.2 RecursiveMethod for Calculating Estimates of Autoregressive Parameters87

4 LINEAR NONSTATIONARY MODELS89

4.1 Autoregressive Integrated Moving Average Processes89

4.1.1 Nonstationary First-Order Autoregressive Process89

4.1.2 General Model for a Nonstationary Process Exhibiting Homogeneity92

4.1.3 General Form of the Autoregressive Integrated Moving A verage Process96

4.2 Three Explicit Forms for the Autoregressive Integrated Moving Average Model99

4.2.1 Difference Equation Form ofthe Model99

4.2.2 Random Shock Form ofthe Model100

4.2.3 Inverted Form of the Model106

4.3 Integrated Moving Average Processes109

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 Difierence Equations120

A4.2 IMA(0,1,1)Process With Deterministic Drift125

A4.3 ARIMA Processes With Added Noise126

A4.3.1 Sum of Two Independent Moving Average Processes126

A4.3.2 Effect ofAdded Noise on the General Model127

A4.3.3 Example for an IMA(0,1,1)Process with Added White Noise128

A4.3.4 Relation Between the IMA(0,1,1) Process and a Random Walk129

A4.3.5 Autocovariance Function of the General Model with Added Correlated Noise129

5 FORECASTING131

5.1 Minimum Mean Square Error Forecasts and Their Properties131

5.1.1 Derivation of the Minimum Mean Square Error Forecasts133

5.1.2 Three Basic Forms for the Forecast135

5.2 Calculating and Updating Forecasts139

5.2.1 Convenient Format for the Forecasts139

5.2.2 Calculation of theψWeights139

5.2.3 Use ofthe ψWeights in Updating the Forecasts141

5.2.4 Calculation of the Probability Limits of the ForecastsatAny Lead Time142

5.3 Forecast Function and Forecast Weights145

5.3.1 Eventual Forecast Function Determined by the Autoregressive Operator146

5.3.2 Role of the Moving Average Operator in Fixing the Initial Values147

5.3.3 Lead l Forecast Weights148

5.4 Examples of Forecast Functions and Their Updating151

5.4.1 Forecasting an IMA(0,1,1) Process151

5.4.2 Forecasting an IMA(0,2,2)Process154

5.4.3 Forecasting a GeneralIMA(0,d,q)Process156

5.4.4 Forecasting Autoregressive Processes157

5.4.5 Forecasting a(1,0,1)Process160

5.4.6 Forecasting a(1,1,1)Process162

5.5 Use of State Space Model Formulation for Exact Forecasting163

5.5.1 State Space Model Representation for the ARIMA Process163

5.5.2 Kalman Filtering Relations for Use in Prediction164

5.6 Summary166

A5.1 Correlations Between Forecast Errors169

A5.1.1 Autocorrelation Function of Forecast Errors at Different Origins169

A5.1.2 Correlation Between Forecast Errors at the Same Origin with Different Lead Times170

A5.2 Forecast Weights for Any Lead Time172

A5.3 Forecasting in Terms of the General Integrated Form174

A5.3.1 General Method of Obtaining the Integrated Form174

A5.3.2 Updating the General Integrated Form176

A5.3.3 Comparison with the Discounted Least Squares Method176

Part Ⅱ Stochastic Model Building181

6 MODELIDENTIFICATION183

6.1 Obiectives of Identification183

6.1.1 Stages in the Identification Procedure184

6.2 Identification Techniques184

6.2.1 Use of the Autocorrelation and Partial Autocorrelation Functions in Identification184

6.2.2 Standard Errors for Estimated Autocorrelations and Partial Autocorrelations188

6.2.3 Identification of Some Actual Time Series188

6.2.4 Some Additional Model Identification Tools197

6.3 Initial Estimates for the Parameters202

6.3.1 Uniqueness of Estimates Obtained from the Autocovariance Function202

6.3.2 Initial Estimates for Moving Average Processes202

6.3.3 Initial Estimates for Autoregressive Processes204

6.3.4 Initial Estimates for Mixed Autoregressive-Moving Average Processes206

6.3.5 Choice Between Stationary and Nonstationary Models in Doubtful Cases207

6.3.6 More Formal Tests for Unit Roots in ARIMA Models208

6.3.7 Initial Estimate of Residual Variance211

6.3.8 Approximate Standard Error for ？212

6.4 Model Multiplicity214

6.4.1 Multiplicity of Autoregressive-Moving Average Models214

6.4.2 Multiple Moment Solutions for Moving Average Parameters216

6.4.3 Use of the Backward Process to Determine Starting Values218

A6.1 Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process218

A6.2 General Method for Obtaining Initial Estimates of the Parameters of a Mixed Autoregressive-Moving Average Process220

7 MODEL ESTIMATION224

7.1 Study of the Likelihood and Sum of Squares Functions224

7.1.1 Likelihood Function224

7.1.2 Conditional Likelihood for an ARIMA Process226

7.1.3 Choice of Starting Values for Conditional Calculation227

7.1.4 Unconditional Likelihood;Sum of Squares Function;Least Squares Estimates228

7.1.5 General Procedure for Calculating the Unconditional Sum of Squares233

7.1.6 GraphicalStudy of the Sum of Squares Function238

7.1.7 Description of"Well-Behaved"Estimation Situations,Confidence Regions241

7.2 Nonlinear Estimation248

7.2.1 General Method of Approach248

7.2.2 Numerical Estimates of the Derivatives249

7.2.3 Direct Evaluation of the Derivatives251

7.2.4 General Least Squares Algorithm for the Conditional Model252

7.2.5 Summary of Models Fitted to Series A to F255

7.2.6 Large-Sample Information Matrices and Covariance Estimates256

7.3 Some Estimation Results for Specific Models259

7.3.1 Autoregressite Processes260

7.3.2 Moving Average Processes262

7.3.3 Mixed Processes262

7.3.4 Separation of Linear and Nonlinear Components in Estimation263

7.3.5 Parameter Redundancy264

7.4 Estimation Using Bayes'Theorem267

7.4.1 Bayes'Theorem267

7.4.2 Bayesian Estimation ofParameters269

7.4.3 Autoregressive Processes270

7.4.4 Moving Average Processes272

7.4.5 Mixed processes274

7.5 Likelihood Function Based on The State Space Model275

A7.1 Review of Normal Distribution Theory279

A7.1.1 Partitioning of a Positive-Definite Quadratic Form279

A7.1.2 Two Useful Integrals280

A7.1.3 Normal Distribution281

A7.1.4 Student's t-Distribution283

A7.2 Review of Linear Least Squares Theory286

A7.2.1 Normal Equations286

A7.2.2 Estimation ofResidual Variance287

A7.2.3 Covariance Matrix ofEstimates288

A7.2.4 Confidence Regions288

A7.2.5 Correlated Errors288

A7.3 Exact Likelihood Function for Moving Average and Mixed Processes289

A7.4 Exact Likelihood Function for an Autoregressive Process296

A7.5 Examples of the Effect of Parameter Estimation Errors on Probability Limits for Forecasts304

A7.6 Special Note on Estimation of Moving Average Parameters307

8 MODEL DIAGNOSTIC CHECKING308

8.1 Checking the Stochastic Model308

8.1.1 General Philosophy308

8.1.2 Overfitting309

8.2 Diagnostic Checks Applied to Residuals312

8.2.1 Autocorrelation Check312

8.2.2 Portmanteau Lack-of-Fit Test314

8.2.3 Model Inadequacy Arising from Changes in Parameter values317

8.2.4 Score Tests for Model Checking318

8.2.5 Cumulative Periodogram Check321

8.3 Use of Residuals to Modify the Model324

8.3.1 Nature of the Correlations in the Residuals When an Incorrect Model Is Used324

8.3.2 Use of Residuals to Modify the Model325

9 SEASONAL MODELS327

9.1 Parsimonious Models for Seasonal Time Series327

9.1.1 Fitting versus Forecasting328

9.1.2 Seasonal Models Involving Adaptive Sines and Cosines329

9.1.3 General Multiplicative Seasonal Model330

9.2 Representation of the Airline Data by a Multiplicative (0,1,1)×(0,1,1)12 Seasonal Model333

9.2.1 Multiplicative(0,1,1)x (0,1,1)12 Model333

9.2.2 Forecasting334

9.2.3 Identification341

9.2.4 Estimation344

9.2.5 Diagnostic Checking349

9.3 Some Aspects of More General Seasonal Models351

9.3.1 Multiplicative and Nonmultiplicative Models351

9.3.2 Identification353

9.3.3 Estimation355

9.3.4 Eventual Forecast Functions for Various Seasonal Models355

9.3.5 Choice of Transformation358

9.4 Structural Component Models and Deterministic Seasonal Components359

9.4.1 Deterministic Seasonal and Trend Components and Common Factors360

9.4.2 Models with Regression Terms and Time Series Error Terms361

A9.1 Autocovariances for Some Seasonal Models366

Part Ⅲ Transfer Function Model Building371

10 TRANSFER FUNCTION MODELS373

10.1 Linear Transfer Function Models373

10.1.1 Discrete Transfer Function374

10.1.2 Continuous Dynamic Models Represented by Differential Equations376

10.2 Discrete Dynamic Models Represented by Difference Equations381

10.2.1 General Form of the Difference Equation381

10.2.2 Nature of the Transfer Function383

10.2.3 First-and Second-Order Discrete Transfer Function Models384

10.2.4 Recursive Computation of Output for Any Input390

10.2.5 Transfer Function Models with Added Noise392

10.3 Relation Between Discrete and Continuous Models392

10.3.1 Response to a Pulsed Input393

10.3.2 Relationships for First-and Second-Order Coincident Systems395

10.3.3 Approximating General Continuous Models by Discrete Models398

A10.1 Continuous Models With Pulsed Inputs399

A10.2 Nonlinear Transfer Functions and Linearization404

11 IDENTIFICATION,FITTING,AND CHECKING OF TRANSFER FUNCTION MODELS407

11.1 Cross Correlation Function408

11.1.1 Properties of the Cross Covariance and Cross Correlation Functions408

11.1.2 Estimation of the Cross Covariance and Cross Correlation Functions411

11.1.3 Approximate Standard Errors of Cross Correlation Estimates413

11.2 Identification of Transfer Function Models415

11.2.1 Identification of Transfer Function Models by Prewhitening the Input417

11.2.2 Example ofthe Identification of a Transfer Function Model419

11.2.3 Identification of the Noise Model422

11.2.4 Some General Considerations in Identifying Transfer Function Models424

11.3 Fitting and Checking Transfer Function Models426

11.3.1 Conditional Sum of Squares Function426

11.3.2 Nonlinear Estimation429

11.3.3 Use of Residuals for Diagnostic Checking431

11.3.4 Specific Checks Applied to the Residuals432

11.4 Some Examples of Fitting and Checking Transfer Function Models435

11.4.1 Fitting and Checking of the Gas Furnace Model435

11.4.2 Simulated Example with Two Inputs441

11.5 Forecasting Using Leading Indicators444

11.5.1 Minimum Mean Square Error Forecast444

11.5.2 Forecast ofCO2 Outputfrom Gas Furnace448

11.5.3 Forecast of Nonstationary Sales Data Using a Leading Indicator451

11.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions453

A11.1 Use of Cross Spectral Analysis for Transfer Function Model Identification455

A11.1.1 Identification ofSingle Input Transfer Function Models455

A11.1.2 Identification of Multiple Input Transfer Function Models456

A 11.2 Choice of Input to Provide Optimal Parameter Estimates457

A11.2.1 Design of Optimal Inputs for a Simple System457

A11.2.2 Numerical Example460

12 INTERVENTION ANALYSIS MODELS AND OUTLIER DETECTION462

12.1 Intervention Analysis Methods462

12.1.1 Modelsfor Intervention Analysis462

12.1.2 Example of Intervention Analysis465

12.1.3 Nature of the MLE for a Simple Level Change Parameter Model466

12.2 Outlier Analysis for Time Series469

12.2.1 Models for Additive and Innovational Outliers469

12.2.2 Esti？ation of Outlier Effect for Known Timing of the Outlier470

12.2.3 Iterative Procedure for Outlier Detection471

12.2.4 Examples of Analysis of Outliers473

12.3 Estimation for ARMA Models With Missing Values474

Part Ⅳ Design of Discrete Control Schemes481

13 ASPECTS OF PROCESS CONTROL483

13.1 Process Monitoring and Process Adjustment484

13.1.1 Process Monitoring484

13.1.2 Process Adjustment487

13.2 Process Adjustment Using Feedback Control488

13.2.1 Feedback Adjustment Chart489

13.2.2 Modeling the Feedback Loop492

13.2.3 Simple Models for Disturbances and Dynamics493

13.2.4 General Minimum Mean Square Error Feedback Control Schemes497

13.2.5 Manual Adjustment for Discrete Proportional-Integral Schemes499

13.2.6 Complementary Roles of Monitoring and Adjustment503

13.3 Excessive Adjustment Sometimes Required by MMSE Control505

13.3.1 Constrained Control506

13.4 Minimum Cost Control With Fixed Costs of Adjustment And Monitoring508

13.4.1 Bounded Adjustment Scheme for Fixed Adjustment Cost508

13.4.2 Indirect Approach for Obtaining a Bounded Adjustment Scheme510

13.4.3 Inclusion of the Cost of Monitoring511

13.5 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes514

A13.1 Feedback Control Schemes Where the Adiustment Variance Is Restricted516

A13.1.1 Derivation of Optimal Adjustment517

A13.2 Choice of the Sampling Interval526

A13.2.1 Illustration of the Effect of Reducing Sampling Frequency526

A13.2.2 Sampling an lMA(0,1,1)Process526

Part Ⅴ Charts and Tables531

COLLECTION OF TABLES AND CHARTS533

COLLECTION OF TIME SERIES USED FOR EXAMPLES IN THE TEXT AND IN EXERCISES540

REFERENCES556

Part Ⅵ EXERCISES AND PROBLEMS569

INDEX589