Time series analysis: forecasting and control
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| Main Authors: | , , , |
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| Format: | Book |
| Language: | English |
| Published: |
Hoboken
Wiley
[2016]
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| Edition: | Fifth edition |
| Series: | Wiley series in probability and statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xxvi, 669 Seiten Diagramme |
| ISBN: | 9781118675021 9781118674918 |
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| 100 | 1 | |a Box, George E. P. |d 1919-2013 |0 (DE-588)108415066 |4 aut | |
| 245 | 1 | 0 | |a Time series analysis |b forecasting and control |c George E. P. Box ; Gwilym E. Jenkins ; Gregory C. Reinsel ; Greta M. Ljung |
| 250 | |a Fifth edition | ||
| 264 | 1 | |a Hoboken |b Wiley |c [2016] | |
| 264 | 4 | |c © 2016 | |
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| 490 | 0 | |a Wiley series in probability and statistics | |
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| _version_ | 1804174985289269248 |
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| adam_text | CONTENTS
PREFACE TO THE FIFTH EDITION
PREFACE TO THE FOURTH EDITION
PREFACE TO THE THIRD EDITION
1 Introduction
1.1 Five 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 Analysis of Multivariate Time Series, 4
1.1.5 Discrete Control Systems, 5
1.2 Stochastic and Deterministic Dynamic Mathematical Models, 6
1.2.1 Stationary and Nonstationary Stochastic Models for Forecasting
and Control, 7
1.2.2 Transfer Function Models, 11
1.2.3 Models for Discrete Control Systems, 13
1.3 Basic Ideas in Model Building, 14
1.3. 1 Parsimony, 14
1.3.2 Iterative Stages in the Selection of a Model, 15
Appendix AIT Use of the R Software, 17
Exercises, 18
xix
xxiii
XXV
1
Vll
viii
CONTENTS
PART ONE 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, 24
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 Errors of Autocorrelation Estimates, 31
2.2 Spectral Properties of Stationary Models, 34
2.2.1 Periodogram of a Time Series, 34
2.2.2 Analysis of Variance, 35
2.2.3 Spectrum and Spectral Density Function, 36
2.2.4 Simple Examples of Autocorrelation and Spectral Density
Functions, 40
2.2.5 Advantages and Disadvantages of the Autocorrelation and Spectral
Density Functions, 43
Appendix A2.1 Link Between the Sample Spectrum and Autocovariance
Function Estimate, 43
Exercises, 44
3 Linear Stationary Models 47
3.1 General Linear Process, 47
3.1.1 Two Equivalent Forms for the Linear Process, 47
3.1.2 Autocovariance Generating Function of a Linear Process, 50
3.1.3 Stationarity and Invertibility Conditions for a Linear Process, 51
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 Autoregressive
Processes, 56
3.2.3 The First-Order Autoregressive Process, 58
3.2.4 Second-Order Autoregressive Process, 59
3.2.5 Partial Autocorrelation Function, 64
3.2.6 Estimation of the Partial Autocorrelation Function, 66
3.2.7 Standard Errors of Partial Autocorrelation Estimates, 66
3.2.8 Calculations in R, 67
3.3 Moving Average Processes, 68
3.3.1 Invertibility Conditions for Moving Average Processes, 68
3.3.2 Autocorrelation Function and Spectrum of Moving Average
Processes, 69
3.3.3 First-Order Moving Average Process, 70
3.3.4 Second-Order Moving Average Process, 71
3.3.5 Duality Between Autoregressive and Moving Average Processes, 75
3.4 Mixed Autoregressive-Moving Average Processes, 75
CONTENTS
3.4.1 Stationarity and Invertibility Properties, 75
3.4.2 Autocorrelation Function and Spectrum of Mixed Processes, 77
3.4.3 First Order Autoregressive First-Order Moving Average Process, 78
3.4.4 Summary, 81
Appendix A3.1 Autocovariances, Autocovariance Generating Function, and
Stationarity Conditions for a General Linear Process, 82
Appendix A3.2 Recursive Method for Calculating Estimates of
Autoregressive Parameters, 84
Exercises, 86
4 Linear Nonstationary Models
4.1 Autoregressive Integrated Moving Average Processes, 88
4.1.1 Nonstationary First-Order Autoregressive Process, 88
4.1.2 General Model for a Nonstationary Process Exhibiting
Homogeneity, 90
4.1.3 General Form of the ARIMA Model, 94
4.2 Three Explicit Forms for the ARIMA Model, 97
4.2.1 Difference Equation Form of the Model, 97
4.2.2 Random Shock Form of the Model, 98
4.2.3 Invexted Form of the Model, 103
4.3 Integrated Moving Average Processes, 106
4.3.1 Integrated Moving Average Process of Order (0, 1,1), 107
4.3.2 Integrated Moving Average Process of Order (0, 2, 2), 110
4.3.3 General Integrated Moving Average Process of Order (0, d, q), 114
Appendix A4.1 Linear Difference Equations, 116
Appendix A4.2 IMA(0, 1,1) Process with Deterministic Drift, 121
Appendix A4.3 ARIMA Processes with Added Noise, 122
A4.3.1 Sum of Two Independent Moving Average Processes, 122
A4.3.2 Effect of Added Noise on the General Model, 123
A4.3.3 Example for an IMA(0, 1,1) Process with Added White
Noise, 124
A4.3.4 Relation between the IMA(0, 1, 1) Process and a Random
Walk, 125
A4.3.5 Autocovariance Function of the General Model with Added
Correlated Noise, 125
Exercises, 126
5 Forecasting
5.1 Minimum Mean Square Error Forecasts and Their Properties, 129
5.1.1 Derivation of the Minimum Mean Square Error Forecasts, 131
5.1.2 Three Basic Forms for the Forecast, 132
5.2 Calculating Forecasts and Probability Limits, 135
5.2.1 Calculation of у/ Weights, 135
5.2.2 Use of the у/ Weights in Updating the Forecasts, 136
5.2.3 Calculation of the Probability Limits at Different Lead Times, 137
5.2.4 Calculation of Forecasts Using R, 138
5.3 Forecast Function and Forecast Weights, 139
X
CONTENTS
5.3.1 Eventual Forecast Function Determined by the Autoregressive
Operator, 140
5.3.2 Role of the Moving Average Operator in Fixing the Initial
Values, 140
5.3.3 Lead l Forecast Weights, 142
5.4 Examples of Forecast Functions and Their Updating, 144
5.4.1 Forecasting an IMA(0, 1, 1) Process, 144
5.4.2 Forecasting an IMA(0, 2, 2) Process, 147
5.4.3 Forecasting a General IMA(0, d, q) Process, 149
5.4.4 Forecasting Autoregressive Processes, 150
5.4.5 Forecasting a (1, 0, 1) Process, 153
5.4.6 Forecasting a (1, 1, 1) Process, 154
5.5 Use of State-Space Model Formulation for Exact Forecasting, 155
5.5.1 State-Space Model Representation for the ARIMA Process, 155
5.5.2 Kalman Filtering Relations for Use in Prediction, 157
5.5.3 Smoothing Relations in the State Variable Model, 160
5.6 Summary, 162
Appendix A5.1 Correlation Between Forecast Errors, 164
A5.1.1 Autocorrelation Function of Forecast Errors at Different
A5.1.2
Appendix A5.2
Appendix A5.3
A5.3.1
A5.3.2
A5.3.3
Exercises, 174
Origins, 164
Correlation Between Forecast Errors at the Same Origin with
Different Lead Times, 165
Forecast Weights for any Lead Time, 166
Forecasting in Terms of the General Integrated Form, 168
General Method of Obtaining the Integrated Form, 168
Updating the General Integrated Form, 170
Comparison with the Discounted Least-Squares Method, 171
PART TWO STOCHASTIC MODEL BUILDING
6 Model Identification
6.1 Objectives of Identification, 179
6.1.1 Stages in the Identification Procedure, 180
6.2 Identification Techniques, 180
6.2.1 Use of the Autocorrelation and Partial Autocorrelation Functions
in Identification, 180
6.2.2 Standard Errors for Estimated Autocorrelations and Partial
Autocorrelations, 183
6.2.3 identification of Models for Some Actual Time Series, 185
6.2.4 Some Additional Model Identification Tools, 190
6.3 Initial Estimates for the Parameters, 194
6.3.1 Uniqueness of Estimates Obtained from the Autocovariance
Function, 194
6.3.2 Initial Estimates for Moving Average Processes, 194
6.3.3 Initial Estimates for Autoregressive Processes, 196
CONTENTS
6.3.4 Initial Estimates for Mixed Autoregressive-Moving Average
Processes, 197
6.3.5 Initial Estimate of Error Variance, 198
6.3.6 Approximate Standard Error for To, 199
6.3.7 Choice Between Stationary and Nonstationary Models in Doubtful
Cases, 200
6.4 Model Multiplicity, 202
6.4.1 Multiplicity of Autoregressive-Moving Average Models, 202
6.4.2 Multiple Moment Solutions for Moving Average Parameters, 204
6.4.3 Use of the Backward Process to Determine Starting Values, 205
Appendix A6.1 Expected Behavior of the Estimated Autocorrelation Function
for a Nonstationary Process, 206
Exercises, 207
7 Parameter Estimation
7.1 Study of the Likelihood and Sum~of֊Squares Functions, 209
7.1.1 Likelihood Function, 209
7.1.2 Conditional Likelihood for an ARI1V1A Process, 210
7.1.3 Choice of Starting Values for Conditional Calculation, 211
7.1.4 Unconditional Likelihood, Sum-of Squares Function, and
Least-Squares Estimates, 213
7.1.5 General Procedure for Calculating the Unconditional Sum of
Squares, 216
7.1.6 Graphical Study of the Sum-of-Squares Function, 218
7.1.7 Examination of the Likelihood Function and Confidence
Regions, 220
7.2 Nonlinear Estimation, 226
7.2.1 General Method of Approach, 226
7.2.2 Numerical Estimates of the Derivatives, 227
7.2.3 Direct Evaluation of the Derivatives, 228
7.2.4 General Least-Squares Algorithm for the Conditional Model, 229
7.2.5 ARIMA Models Fitted to Series A-F, 231
7.2.6 Large-Sample Information Matrices and Covariance Estimates, 233
7.3 Some Estimation Results for Specific Models, 236
7.3.1 Autoregressive Processes, 236
7.3.2 Moving Average Processes, 238
7.3.3 Mixed Processes, 238
7.3.4 Separation of Linear and Nonlinear Components in Estimation, 239
7.3.5 Parameter Redundancy, 240
7.4 Likelihood Function Based on the State-Space Model, 242
7.5 Estimation Using Bayes’ Theorem, 245
7.5.1 Bayes’ Theorem, 245
7.5.2 Bayesian Estimation of Parameters, 246
7.5.3 Autoregressive Processes, 247
7.5.4 Moving Average Processes, 249
7.5.5 Mixed Processes, 250
Appendix A7.1 Review of Normal Distribution Theory, 251
xii
CONTENTS
A7.1.1 Partitioning of a Positive-Definite Quadratic Form, 251
A7.1.2 Two Useful Integrals, 252
A7.1.3 Normal Distribution, 253
A7.1.4 Student’s t Distribution, 255
Appendix A7.2 Review of Linear Least-Squares Theory, 256
A7.2.1 Normal Equations and Least Squares, 256
hi 2.2 Estimation of Error Variance, 257
hi2.3 Covariance Matrix of Least-Squares Estimates, 257
hi 2.4 Confidence Regions, 257
hi2.5 Correlated Errors, 258
Appendix hi .3 Exact Likelihood Function for Moving Average and Mixed
Processes, 259
Appendix A7.4 Exact Likelihood Function for an Autoregressive Process, 266
Appendix hi.5 Asymptotic Distribution of Estimators for Autoregressive
Models, 274
Appendix hi.6 Examples of the Effect of Parameter Estimation Errors on
Variances of Forecast Errors and Probability Limits for Forecasts, 277
Appendix hi.1 Special Note on Estimation of Moving Average Parameters, 280
Exercises, 280
8 Model Diagnostic Checking 284
8Л Checking the Stochastic Model, 284
8ЛЛ General Philosophy, 284
8.1.2 Overfitting, 285
8.2 Diagnostic Checks Applied to Residuals, 287
8.2Л Autocorrelation Check, 287
8.2.2 Portmanteau Lack-of-Fit Test, 289
8.2.3 Model Inadequacy Arising from Changes in Parameter Values, 294
8.2.4 Score Tests for Model Checking, 295
8.2.5 Cumulative Periodogram Check, 297
8.3 Use of Residuals to Modify the Model, 301
8.3.1 Nature of the Correlations in the Residuals When an Incorrect
Model Is Used, 301
8.3.2 Use of Residuals to Modify the Model, 302
Exercises, 303
9 Analysis of Seasonal Time Series
9.1 Parsimonious Models for Seasonal Time Series, 305
9.1 Л Fitting Versus Forecasting, 306
9.1.2 Seasonal Models Involving Adaptive Sines and Cosines, 307
9.1.3 General Multiplicative Seasonal Model, 308
9.2 Representation of the Airline Data by a Multiplicative (0, 1,1) X (0,1, l)i2
Model, 310
9.2.1 Multiplicative (0,1,1) X (0,1,1)12 Model, 310
9.2.2 Forecasting, 311
9.2.3 Model Identification, 318
9.2.4 Parameter Estimation, 320
CONTENTS
xiii
9.2.5 Diagnostic Checking, 324
9.3 Some Aspects of More General Seasonal ARIMA Models, 325
9.3.1 Multiplicative and Nonmultiplicative Models, 325
9.3.2 Model Identification, 327
9.3.3 Parameter Estimation, 328
9.3.4 Eventual Forecast Functions for Various Seasonal Models, 329
9.3.5 Choice of Transformation, 331
9.4 Structural Component Models and Deterministic Seasonal
Components, 331
9.4.1 Structural Component Time Series Models, 332
9.4.2 Deterministic Seasonal and Trend Components and Common
Factors, 335
9.4.3 Estimation of Unobserved Components in Structural Models, 336
9.5 Regression Models with Time Series Error Terms, 339
9.5.1 Model Building, Estimation, and Forecasting Procedures for
Regression Models, 340
9.5.2 Restricted Maximum Likelihood Estimation for Regression
Models, 344
Appendix A9.1 Autocovariances for Some Seasonal Models, 345
Exercises, 349
10 Additional Topics and Extensions 352
10.1 Tests for Unit Roots in ARIMA Models, 353
10.1.1 Tests for Unit Roots in AR Models, 353
10.1.2 Extensions of Unit Root Testing to Mixed ARIMA Models, 358
10.2 Conditional Heteroscedastic Models, 361
10.2.1 The ARCH Model, 362
10.2.2 The GARCH Model, 366
10.2.3 Model Building and Parameter Estimation, 367
10.2.4 An Illustrative Example: Weekly S P 500 Log Returns, 370
10.2.5 Extensions of the ARCH and GARCH Models, 372
10.2.6 Stochastic Volatility Models, 377
10.3 Nonlinear Time Series Models, 377
10.3.1 Classes of Nonlinear Models, 378
10.3.2 Detection of Nonlinearity, 381
10.3.3 An Empirical Example, 382
10.4 Long Memory Time Series Processes, 385
10.4.1 Fractionally Integrated Processes, 385
10.4.2 Estimation of Parameters, 389
Exercises, 392
PART THREE TRANSFER FUNCTION AND MULTiVAMiAT
MODEL BUILDING
395
IX Transfer Function Models
11.1 Linear Transfer Function Models, 397
397
xiv
CONTENTS
11.1.1 Discrete Transfer Function, 398
11.1.2 Continuous Dynamic Models Represented by Differential
Equations, 400
11.2 Discrete Dynamic Models Represented by Difference Equations, 404
11.2.1 General Form of the Difference Equation, 404
11.2.2 Nature of the Transfer Function, 406
1 L2.3 First- and Second-Order Discrete Transfer Function Models, 407
11.2.4 Recursive Computation of Output for Any Input, 412
11.2.5 Transfer Function Models with Added Noise, 413
11.3 Relation Between Discrete and Continuous Models, 414
11.3.1 Response to a Pulsed Input, 415
11.3.2 Relationships for First- and Second-Order Coincident
Systems, 417
11.3.3 Approximating General Continuous Models by Discrete
Models, 419
Appendix Al 1.1 Continuous Models with Pulsed Inputs, 420
Appendix A11.2 Nonlinear Transfer Functions and Linearization, 424
Exercises, 426
12 Identification, Fitting, and Checking of Transfer Function Models 428
12.1 Cross-Correlation Function, 429
12.1.1 Properties of the Cross-Covariance and Cross-Correlation
Functions, 429
12.1.2 Estimation of the Cross-Covariance and Cross-Correlation
Functions, 431
12.1.3 Approximate Standard Errors of Cross-Correlation
Estimates, 433
12.2 Identification of Transfer Function Models, 435
12.2.1 Identification of Transfer Function Models by Prewhitening the
Input, 437
12.2.2 Example of the Identification of a Transfer Function Model, 438
12.2.3 Identification of the Noise Model, 442
12.2.4 Some General Considerations in Identifying Transfer Function
Models, 444
12.3 Fitting and Checking Transfer Function Models, 446
12.3.1 Conditional Sum-of-Squares Function, 446
12.3.2 Nonlinear Estimation, 447
12.3.3 Use of Residuals for Diagnostic Checking, 449
12.3.4 Specific Checks Applied to the Residuals, 450
12.4 Some Examples of Fitting and Checking Transfer Function Models, 453
12.4.1 Fitting and Checking of the Gas Furnace Model, 453
12.4.2 Simulated Example with Two Inputs, 458
12.5 Forecasting with Transfer Function Models Using Leading Indicators, 461
12.5.1 Minimum Mean Square Error Forecast, 461
12.5.2 Forecast of C02 Output from Gas Furnace, 465
12.5.3 Forecast of Nonstationary Sales Data Using a Leading
Indicator, 468
CONTENTS
12.6 Some Aspects of the Design of Experiments to Estimate Transfer
Functions, 469
Appendix A12.1 Use of Cross-Spectral Analysis for Transfer Function Model
Identification, 471
A12.1.1 Identification of Single-Input Transfer Function Models, 471
A12.1.2 Identification of Multiple-Input Transfer Function Models, 472
Appendix A 12.2 Choice of Input to Provide Optimal Parameter Estimates, 473
A 12.2.1 Design of Optimal Inputs for a Simple System, 473
A12.2.2 Numerical Example, 476
Exercises, 477
13 Intervention Analysis, Outlier Detection, and Missing Values
13.1 Intervention Analysis Methods, 481
13.1.1 Models for Intervention Analysis, 481
13.1.2 Example of Intervention Analysis, 484
13.1.3 Nature of the MLE for a Simple Level Change Parameter
Model, 485
13.2 Outlier Analysis for Time Series, 488
13.2.1 Models for Additive and Innovational Outliers, 488
13.2.2 Estimation of Outlier Effect for Known Timing of the Outlier, 489
13.2.3 Iterative Procedure for Outlier Detection, 491
13.2.4 Examples of Analysis of Outliers, 492
13.3 Estimation for ARMA Models with Missing Values, 495
13.3.1 State-Space Model and Kalman Filter with Missing Values, 496
13.3.2 Estimation of Missing Values of an ARMA Process, 498
Exercises, 502
14 Multivariate Time Series Analysis
14.1 Stationary Multivariate Time Series, 506
14.1.1 Cross-Covariance and Cross-Correlation Matrices, 506
14.1.2 Covariance Stationarity, 507
14.1.3 Vector White Noise Process, 507
14.1.4 Moving Average Representation of a Stationary Vector
Process, 508
14.2 Vector Autoregressive Models, 509
14.2.1 VAR(p) Model, 509
14.2.2 Moment Equations and Yule-Walker Estimates, 510
14.2.3 Special Case: VAR( 1) Model, 511
14.2.4 Numerical Example, 513
14.2.5 Initial Model Building and Least-Squares Estimation for VAR
Models, 515
14.2.6 Parameter Estimation and Model Checking, 518
14.2.7 An Empirical Example, 519
14.3 Vector Moving Average Models, 524
14.3.1 Vector MA(#) Model, 524
14.3.2 Special Case: Vector MA(1) Model, 525
14.3.3 Numerical Example, 525
xvi
CONTENTS
14.3.4 Model Building for Vector MA Models, 526
14.4 Vector Autoregressive-Moving Average Models, 527
14.4.1 Stationarity and Invertibility Conditions, 527
14.4.2 Covariance Matrix Properties of V ARM A Processes, 528
14.4.3 Nonuniqueness and Parameter Identifiability for VARMA
Models, 528
14.4.4 Model Specification for VARMA Processes, 529
14.4.5 Estimation and Model Checking for VARMA Models, 532
14.4.6 Relation of VARMA Models to Transfer Function and ARMAX
Models, 533
14.5 Forecasting for Vector Autoregressive-Moving Average Processes, 534
14.5.1 Calculation of Forecasts from ARMA Difference Equation, 534
14.5.2 Forecasts from Infinite VMA Form and Properties of Forecast
Errors, 536
14.6 State-Space Form of the VARMA Model, 536
14.7 Further Discussion of VARMA Model Specification, 539
14.7.1 Kronecker Structure for VARMA Models, 539
14.7.2 An Empirical Example, 543
14.7.3 Partial Canonical Correlation Analysis for Reduced-Rank
Structure, 545
14.8 Nonstationarity and Cointegration, 546
14.8.1 Vector ARIMA Models, 546
14.8.2 Cointegration in Nonstationary Vector Processes, 547
14.8.3 Estimation and Inferences for Cointegrated VAR Models, 549
Appendix A 14.1 Spectral Characteristics and Linear Filtering Relations for
Stationary Multivariate Processes, 552
A14.1.1 Spectral Characteristics for Stationary Multivariate
Processes, 552
A14.1.2 Linear Filtering Relations for Stationary Multivariate
Processes, 553
Exercises, 554
PART FOUR DESIGN OF DISCRETE CONTROL SCHEMES
15 Aspects of Process Control
15.1 Process Monitoring and Process Adjustment, 562
15.1.1 Process Monitoring, 562
15.1.2 Process Adjustment, 564
15.2 Process Adjustment Using Feedback Control, 566
15.2.1 Feedback Adjustment Chart, 567
15.2.2 Modeling the Feedback Loop, 569
15.2.3 Simple Models for Disturbances and Dynamics, 570
15.2.4 General Minimum Mean Square Error Feedback Control
Schemes, 573
15.2.5 Manual Adjustment for Discrete Proportional-Integral
Schemes, 575
CONTENTS
xvii
15.2.6 Complementary Roles of Monitoring and Adjustment, 578
15.3 Excessive Adjustment Sometimes Required by MMSE Control, 580
15.3.1 Constrained Control, 581
15.4 Minimum Cost Control with Fixed Costs of Adjustment and
Monitoring, 582
15.4.1 Bounded Adjustment Scheme for Fixed Adjustment Cost, 583
15.4.2 Indirect Approach for Obtaining a Bounded Adjustment
Scheme, 584
15.4.3 Inclusion of the Cost of Monitoring, 585
15.5 Feedforward Control, 588
15.5.1 Feedforward Control to Minimize Mean Square Error at the
Output, 588
15.5.2 An Example: Control of the Specific Gravity of an Intermediate
Product, 591
15.5.3 Feedforward Control with Multiple Inputs, 593
15.5.4 Feedforward-Feedback Control, 594
15.5.5 Advantages and Disadvantages of Feedforward and Feedback
Control, 596
15.5.6 Remarks on Fitting Transfer Function-Noise Models Using
Operating Data, 597
15.6 Monitoring Values of Parameters of Forecasting and Feedback
Adjustment Schemes, 599
Appendix A15.1 Feedback Control Schemes Where the Adjustment Variance
Is Restricted, 600
A15.1.1 Derivation of Optimal Adjustment, 601
A15.1.2 Case Where S Is Negligible, 603
Appendix A 15.2 Choice of the Sampling Interval, 609
A 15.2.1 Illustration of the Effect of Reducing Sampling Frequency, 610
A 15.2.2 Sampling an IMA(0,1,1) Process, 610
Exercises, 613
PART FIVE CHARTS AND TABLES 617
COLLECTION OF TABLES AND CHARTS 619
COLLECTION OF TIME SERIES USED FOR EX TEXT AND IN EXERCISES AMIPiuES IN THE 625
REFERENCES 642
INDEX 659
|
| any_adam_object | 1 |
| author | Box, George E. P. 1919-2013 Jenkins, Gwilym M. 1932-1982 Reinsel, Gregory C. 1948-2004 Ljung, Greta M. 1941- |
| author_GND | (DE-588)108415066 (DE-588)131749374 (DE-588)113599382 (DE-588)1081748745 |
| author_facet | Box, George E. P. 1919-2013 Jenkins, Gwilym M. 1932-1982 Reinsel, Gregory C. 1948-2004 Ljung, Greta M. 1941- |
| author_role | aut aut aut aut |
| author_sort | Box, George E. P. 1919-2013 |
| author_variant | g e p b gep gepb g m j gm gmj g c r gc gcr g m l gm gml |
| building | Verbundindex |
| bvnumber | BV042764285 |
| classification_rvk | QH 237 SK 845 |
| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)923448270 (DE-599)BVBBV042764285 |
| dewey-full | 519.5/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 |
| dewey-search | 519.5/5 |
| dewey-sort | 3519.5 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Fifth edition |
| format | Book |
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| id | DE-604.BV042764285 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:09:05Z |
| institution | BVB |
| isbn | 9781118675021 9781118674918 |
| language | English |
| lccn | 015015492 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028194739 |
| oclc_num | 923448270 |
| open_access_boolean | |
| owner | DE-739 DE-634 DE-29T DE-20 DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-945 DE-706 DE-83 DE-573 |
| owner_facet | DE-739 DE-634 DE-29T DE-20 DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-945 DE-706 DE-83 DE-573 |
| physical | xxvi, 669 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Box, George E. P. 1919-2013 (DE-588)108415066 aut Time series analysis forecasting and control George E. P. Box ; Gwilym E. Jenkins ; Gregory C. Reinsel ; Greta M. Ljung Fifth edition Hoboken Wiley [2016] © 2016 xxvi, 669 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Stochastisches Modell (DE-588)4057633-4 s 1\p DE-604 Dynamisches System (DE-588)4013396-5 s 2\p DE-604 Stochastik (DE-588)4121729-9 s 3\p DE-604 Jenkins, Gwilym M. 1932-1982 (DE-588)131749374 aut Reinsel, Gregory C. 1948-2004 (DE-588)113599382 aut Ljung, Greta M. 1941- (DE-588)1081748745 aut Erscheint auch als Online-Ausgabe 978-1-118-67491-8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028194739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Box, George E. P. 1919-2013 Jenkins, Gwilym M. 1932-1982 Reinsel, Gregory C. 1948-2004 Ljung, Greta M. 1941- Time series analysis forecasting and control Dynamisches System (DE-588)4013396-5 gnd Stochastik (DE-588)4121729-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4121729-9 (DE-588)4067486-1 (DE-588)4057633-4 |
| title | Time series analysis forecasting and control |
| title_auth | Time series analysis forecasting and control |
| title_exact_search | Time series analysis forecasting and control |
| title_full | Time series analysis forecasting and control George E. P. Box ; Gwilym E. Jenkins ; Gregory C. Reinsel ; Greta M. Ljung |
| title_fullStr | Time series analysis forecasting and control George E. P. Box ; Gwilym E. Jenkins ; Gregory C. Reinsel ; Greta M. Ljung |
| title_full_unstemmed | Time series analysis forecasting and control George E. P. Box ; Gwilym E. Jenkins ; Gregory C. Reinsel ; Greta M. Ljung |
| title_short | Time series analysis |
| title_sort | time series analysis forecasting and control |
| title_sub | forecasting and control |
| topic | Dynamisches System (DE-588)4013396-5 gnd Stochastik (DE-588)4121729-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Dynamisches System Stochastik Zeitreihenanalyse Stochastisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028194739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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