Time series analysis: forecasting and control
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
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Hoboken, NJ
Wiley
2008
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| Ausgabe: | 4. ed. |
| Schriftenreihe: | Wiley series in probability and statistics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 685 - 699 |
| Beschreibung: | XXIV, 746 S. Ill., graph. Darst. |
| ISBN: | 9780470272848 9781118619193 |
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| 650 | 4 | |a Feedback control systems |x Mathematical models | |
| 650 | 4 | |a Prediction theory | |
| 650 | 4 | |a Time-series analysis | |
| 650 | 4 | |a Transfer functions | |
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Datensatz im Suchindex
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| adam_text | 1 TIME SERIES ANALYSIS FORECASTING AND GONTROL FOURTH EDITION GEORGE E.
P. BOX GWILYM M. JENKINS GREGORY C. REINSEL WILEY A JOHN WILEY & SONS,
INC., PUBLICATION CONTENTS PREFACE TO THE FOURTH EDITION XXI PREFACE TO
THE THIRD EDITION XXIII 1 INTRODUCTION 1 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, 5
1.1.5 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, 17 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 VII VIII CONTENTS 2.1.3 POSITIVE
DEFINITENESS AND THE AUTOCOVARIANCE MATRIX, 25 2.1.4 AUTOCOVARIANCE AND
AUTOCORRELATION FUNCTIONS, 29 2.1.5 ESTIMATION OF AUTOCOVARIANCE AND
AUTOCORRELATION FUNCTIONS, 31 2.1.6 STANDARD ERRORS OF AUTOCORRELATION
ESTIMATES, 33 2.2 SPECTRAL PROPERTIES OF STATIONARY MODELS, 35 2.2.1
PERIODOGRAM OF A TIME SERIES, 35 2.2.2 ANALYSIS OF VARIANCE, 37 2.2.3
SPECTRUM AND SPECTRAL DENSITY FUNCTION, 38 2.2.4 SIMPLE EXAMPLES OF
AUTOCORRELATION AND SPECTRAL DENSITY FUNCTIONS, 43 2.2.5 ADVANTAGES AND
DISADVANTAGES OF THE AUTOCORRELATION AND SPECTRAL DENSITY FUNCTIONS, 45
A2.1 LINK BETWEEN THE SAMPLE SPECTRUM AND AUTOCOVARIANCE FUNCTION
ESTIMATE, 45 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, 53 3.2 AUTOREGRESSIVE
PROCESSES, 55 3.2.1 STATIONARITY CONDITIONS FOR AUTOREGRESSIVE
PROCESSES, 55 3.2.2 AUTOCORRELATION FUNCTION AND SPECTRUM OF
AUTOREGRESSIVE PROCESSES, 57 3.2.3 FIRST-ORDER AUTOREGRESSIVE (MARKOV)
PROCESS, 59 3.2.4 SECOND-ORDER AUTOREGRESSIVE PROCESS, 61 3.2.5 PARTIAL
AUTOCORRELATION FUNCTION, 66 3.2.6 ESTIMATION OF THE PARTIAL
AUTOCORRELATION FUNCTION, 69 3.2.7 STANDARD ERRORS OF PARTIAL
AUTOCORRELATION ESTIMATES, 70 3.3 MOVING AVERAGE PROCESSES, 71 CONTENTS
IX 3.3.1 INVERTIBILITY CONDITIONS FOR MOVING AVERAGE PROCESSES, 71 3.3.2
AUTOCORRELATION FUNCTION AND SPECTRUM OF MOVING AVERAGE PROCESSES, 72
3.3.3 FIRST-ORDER MOVING AVERAGE PROCESS, 73 3.3.4 SECOND-ORDER MOVING
AVERAGE PROCESS, 75 3.3.5 DUALITY BETWEEN AUTOREGRESSIVE AND MOVING
AVERAGE PROCESSES, 78 3.4 MIXED AUTOREGRESSIVE-MOVING AVERAGE PROCESSES,
79 3.4.1 STATIONARITY AND INVERTIBILITY PROPERTIES, 79 3.4.2
AUTOCORRELATION FUNCTION AND SPECTRUM OF MIXED PROCESSES, 80 3.4.3
FIRST-ORDER AUTOREGRESSIVE-FIRST-ORDER MOVING AVERAGE PROCESS, 82 3.4.4
SUMMARY, 86 A3.1 AUTOCOVARIANCES, AUTOCOVARIANCE GENERATING FUNCTION,
AND STATIONARITY CONDITIONS FOR A GENERAL LINEAR PROCESS, 86 A3.2
RECURSIVE METHOD FOR CALCULATING ESTIMATES OF AUTOREGRESSIVE PARAMETERS,
89 4 LINEAR NONSTATIONARY MODELS 4.1 AUTOREGRESSIVE INTEGRATED MOVING
AVERAGE PROCESSES, 93 4.1.1 NONSTATIONARY FIRST-ORDER AUTOREGRESSIVE
PROCESS, 93 4.1.2 GENERAL MODEL FOR A NONSTATIONARY PROCESS EXHIBITING
HOMOGENEITY, 95 4.1.3 GENERAL FORM OF THE AUTOREGRESSIVE INTEGRATED
MOVING AVERAGE MODEL, 100 4.2 THREE EXPLICIT FORMS FOR THE
AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL, 103 . - 4.2.1
DIFFERENCE EQUATION FORM OF THE MODEC 103 4.2.2 RANDOM SHOCK FORM OF THE
MODEL, 104 4.2.3 INVERTED FORM OF THE MODEL, 111 4.3 INTEGRATED MOVING
AVERAGE PROCESSES, 114 4.3.1 INTEGRATED MOVING AVERAGE PROCESS OF ORDER
(0, 1, 1), 115 4.3.2 INTEGRATED MOVING AVERAGE PROCESS OF ORDER (0, 2,
2), 119 4.3.3 GENERAL INTEGRATED MOVING AVERAGE PROCESS OF ORDER (0, D,
Q), 123 A4.1 LINEAR DIFFERENCE EQUATIONS, 125 A4.2 IMA(0, 1,1) PROCESS
WITH DETERMINISTIC DRIFT, 131 93 K CONTENTS A4.3 ARIMA PROCESSES WITH
ADDED NOISE, 131 A4.3.1 SUM OF TWO INDEPENDENT MOVING AVERAGE PROCESSES,
132 A4.3.2 EFFECT OF ADDED NOISE ON THE GENERAL MODEL, 133 A4.3.3
EXAMPLE FOR AN IMA(0, 1, 1) PROCESS WITH ADDED WHITE NOISE, 134 A4.3.4
RELATION BETWEEN THE IMA(0, 1,1) PROCESS AND A RANDOM WALK, 135 A4.3.5
AUTOCOVARIANCE FUNCTION OF THE GENERAL MODEL WITH ADDED CORRELATED
NOISE, 135 5 FORECASTING 137 5.1 MINIMUM MEAN SQUARE ERROR FORECASTS AND
THEIR PROPERTIES, 137 5.1.1 DERIVATION OF THE MINIMUM MEAN SQUARE ERROR
FORECASTS, 139 5.1.2 THREE BASIC FORMS FOR THE FORECAST, 141 5.2
CALCULATING AND UPDATING FORECASTS, 145 5.2.1 CONVENIENT FORMAT FOR THE
FORECASTS, 145 5.2.2 CALCULATION OF THE ^ WEIGHTS, 147 5.2.3 USE OF THE
JR WEIGHTS IN UPDATING THE FORECASTS, 148 5.2.4 CALCULATION OF THE
PROBABILITY LIMITS OF THE FORECASTS AT ANY LEAD TIME, 150 5.3 FORECAST
FUNCTION AND FORECAST WEIGHTS, 152 5.3.1 EVENTUAL FORECAST FUNCTION
DETERMINED BY THE AUTOREGRESSIVE OPERATOR, 152 5.3.2 ROLE OF THE MOVING
AVERAGE OPERATOR IN FIXING THE INITIAL VALUES, 153 5.3.3 LEAD / FORECAST
WEIGHTS, 154 5.4 EXAMPLES OF FORECAST FUNCTIONS AND THEIR UPDATING, 157
5.4.1 FORECASTING AN IMA(0, 1, 1) PROCESS, 157 5.4.2 FORECASTING AN
IMA(0, 2, 2) PROCESS, 160 5.4.3 FORECASTING A GENERAL IMA(0, D, Q)
PROCESS, 163 5.4.4 FORECASTING AUTOREGRESSIVE PROCESSES, 164 5.4.5
FORECASTING A (1, 0, 1) PROCESS, 167 5.4.6 FORECASTING A (1, 1, 1)
PROCESS, 169 T CONTENTS XI 5.5 USE OF STATE-SPACE MODEL FORMULATION FOR
EXACT FORECASTING, 170 5.5.1 STATE-SPACE MODEL REPRESENTATION FOR THE
ARIMA PROCESS, 170 5.5.2 KALMAN FILTERING RELATIONS FOR USE IN
PREDICTION, 171 5.5.3 SMOOTHING RELATIONS IN THE STATE VARIABLE MODEL,
175 5.6 SUMMARY, 177 A5.1 CORRELATIONS BETWEEN FORECAST ERRORS, 180
A5.1.1 AUTOCORRELATION FUNCTION OF FORECAST ERRORS AT DIFFERENT ORIGINS,
180 A5.1.2 CORRELATION BETWEEN FORECAST ERRORS AT THE SAME ORIGIN WITH
DIFFERENT LEAD TIMES, 182 A5.2 FORECAST WEIGHTS FOR ANY LEAD TIME, 182
A5.3 FORECASTING IN TERMS OF THE GENERAL INTEGRATED FORM, 185 A5.3.1
GENERAL METHOD OF OBTAINING THE INTEGRATED FORM, 185 A5.3.2 UPDATING THE
GENERAL INTEGRATED FORM, 187 A5.3.3 COMPARISON WITH THE DISCOUNTED LEAST
SQUARES METHOD, 187 PART TWO STOCHASTIC MODEL BUILDING 193 6 MODEL
IDENTIFICATION 195 6.1 OBJECTIVES OF IDENTIFICATION, 195 6.1.1 STAGES IN
THE IDENTIFICATION PROCEDURE, 195 6.2 IDENTIFICATION TECHNIQUES, 196
6.2.1 USE OF THE AUTOCORRELATION AND PARTIAJL^.^ AUTOCORRELATION
FUNCTIONS IN IDENTIFICATION, 196 6.2.2 STANDARD ERRORS FOR ESTIMATED
AUTOCORRELATIONS AND PARTIAL AUTOCORRELATIONS, 198 6.2.3 IDENTIFICATION
OF SOME ACTUAL TIME SERIES, 200 6.2.4 SOME ADDITIONAL MODEL
IDENTIFICATION TOOLS, 208 6.3 INITIAL ESTIMATES FOR THE PARAMETERS, 213
6.3.1 UNIQUENESS OF ESTIMATES OBTAINED FROM THE AUTOCOVARIANCE FUNCTION,
213 6.3.2 INITIAL ESTIMATES FOR MOVING AVERAGE PROCESSES, 213 6.3.3
INITIAL ESTIMATES FOR AUTOREGRESSIVE PROCESSES, 215 XII CONTENTS 6.3.4
INITIAL ESTIMATES FOR MIXED AUTOREGRESSIVE-MOVING AVERAGE PROCESSES, 216
6.3.5 INITIAL ESTIMATE OF ERROR VARIANCE, 218 6.3.6 APPROXIMATE STANDARD
ERROR FOR W, 218 6.3.7 CHOICE BETWEEN STATIONARY AND NONSTATIONARY
MODELS IN DOUBTFUL CASES, 220 6.4 MODEL MULTIPLICITY, 221 6.4.1
MULTIPLICITY OF AUTOREGRESSIVE-MOVING AVERAGE MODELS, 221 6.4.2 MULTIPLE
MOMENT SOLUTIONS FOR MOVING AVERAGE PARAMETERS, 224 6.4.3 USE OF THE
BACKWARD PROCESS TO DETERMINE STARTING VALUES, 225 A6.1 EXPECTED
BEHAVIOR OF THE ESTIMATED AUTOCORRELATION FUNCTION FOR A NONSTATIONARY
PROCESS, 225 A6.2 GENERAL METHOD FOR OBTAINING INITIAL ESTIMATES OF THE
PARAMETERS OF A MIXED AUTOREGRESSIVE-MOVING AVERAGE PROCESS, 226 7 MODEL
ESTIMATION 231 7.1 STUDY OF THE LIKELIHOOD AND SUM-OF-SQUARES FUNCTIONS,
231 7.1.1 LIKELIHOOD FUNCTION, 231 7.1.2 CONDITIONAL LIKELIHOOD FOR AN
ARIMA PROCESS, 232 7.1.3 CHOICE OF STARTING VALUES FOR CONDITIONAL
CALCULATION, 234 7.1.4 UNCONDITIONAL LIKELIHOOD; SUM-OF-SQUARES
FUNCTION; LEAST SQUARES ESTIMATES, 235 7.1.5 GENERAL PROCEDURE FOR
CALCULATING THE UNCONDITIONAL SUM OF SQUARES, 240 7.1.6 GRAPHICAL
STUDY OF THE SUM-OF-SQUARES FUNCTION, 245 7.1.7 DESCRIPTION OF
WELL-BEHAVED ESTIMATION SITUATIONS; CONFIDENCE REGIONS, 248 7.2
NONLINEAR ESTIMATION, 255 7.2.1 GENERAL METHOD OF APPROACH, 255 7.2.2
NUMERICAL ESTIMATES OF THE DERIVATIVES, 257 7.2.3 DIRECT EVALUATION OF
THE DERIVATIVES, 258 7.2.4 GENERAL LEAST SQUARES ALGORITHM FOR THE
CONDITIONAL MODEL, 260 7.2.5 SUMMARY OF MODELS FITTED TO SERIES A TO F,
263 CONTENTS XIII 7.2.6 LARGE-SAMPLE INFORMATION MATRICES AND COVARIANCE
ESTIMATES, 264 7.3 SOME ESTIMATION RESULTS FOR SPECIFIC MODELS, 268
7.3.1 AUTOREGRESSIVE PROCESSES, 268 7.3.2 MOVING AVERAGE PROCESSES, 270
7.3.3 MIXED PROCESSES, 271 7.3.4 SEPARATION OF LINEAR AND NONLINEAR
COMPONENTS IN ESTIMATION, 271 7.3.5 PARAMETER REDUNDANCY, 273 7.4
LIKELIHOOD FUNCTION BASED ON THE STATE-SPACE MODEL, 275 7.5 UNIT ROOTS
IN ARIMA MODELS, 280 7.5.1 FORMAL TESTS FOR UNIT ROOTS IN AR MODELS, 281
7.5.2 EXTENSIONS OF UNIT-ROOT TESTING TO MIXED ARIMA MODELS, 286 7.6
ESTIMATION USING BAYES S THEOREM, 287 7.6.1 BAYES S THEOREM, 287 7.6.2
BAYESIAN ESTIMATION OF PARAMETERS, 289 7.6.3 AUTOREGRESSIVE PROCESSES,
290 7.6.4 MOVING AVERAGE PROCESSES, 293 7.6.5 MIXED PROCESSES, 294 A7.1
REVIEW OF NORMAL DISTRIBUTION THEORY, 296 A7.1.1 PARTITIONING OF A
POSITIVE-DEFINITE QUADRATIC FORM, 296 A7.1.2 TWO USEFUL INTEGRALS, 296
A7.1.3 NORMAL DISTRIBUTION, 297 A7.1.4 STUDENT S T DISTRIBUTION, 300
A7.2 REVIEW OF LINEAR LEAST SQUARES THEORY, 303 A7.2.1 NORMAL EQUATIONS
AND LEAST SQUARES, 303^ HI.2.2 ESTIMATION OF ERROR VARIANCE, 3OT A7.2.3
COVARIANCE MATRIX OF LEAST SQUARES ESTIMATES, 305 A7.2.4 CONFIDENCE
REGIONS, 305 A7.2.5 CORRELATED ERRORS, 305 A7.3 EXACT LIKELIHOOD
FUNCTION FOR MOVING AVERAGE AND MIXED PROCESSES, 306 A7.4 EXACT
LIKELIHOOD FUNCTION FOR AN AUTOREGRESSIVE PROCESS, 314 A7.5 ASYMPTOTIC
DISTRIBUTION OF ESTIMATORS FOR AUTOREGRESSIVE MODELS, 323 XIV CONTENTS
A7.6 EXAMPLES OF THE EFFECT OF PARAMETER ESTIMATION ERRORS ON VARIANCES
OF FORECAST ERRORS AND PROBABILITY LIMITS FOR FORECASTS, 327 A7.7
SPECIAL NOTE ON ESTIMATION OF MOVING AVERAGE PARAMETERS, 330 8 MODEL
DIAGNOSTIC CHECKING 333 8.1 CHECKING THE STOCHASTIC MODEL, 333 8.1.1
GENERAL PHILOSOPHY, 333 8.1.2 OVERFITTING, 334 8.2 DIAGNOSTIC CHECKS
APPLIED TO RESIDUALS, 335 8.2.1 AUTOCORRELATION CHECK, 337 8.2.2
PORTMANTEAU LACK-OF-FIT TEST, 338 8.2.3 MODEL INADEQUACY ARISING FROM
CHANGES IN PARAMETER VALUES, 343 8.2.4 SCORE TESTS FOR MODEL CHECKING,
344 8.2.5 CUMULATIVE PERIODOGRAM CHECK, 347 8.3 USE OF RESIDUALS TO
MODIFY THE MODEL, 350 8.3.1 NATURE OF THE CORRELATIONS IN THE RESIDUALS
WHEN AN INCORRECT MODEL IS USED, 350 8.3.2 USE OF RESIDUALS TO MODIFY
THE MODEL, 352 9 SEASONAL MODELS 353 9.1 PARSIMONIOUS MODELS FOR
SEASONAL TIME SERIES, 353 9.1.1 FITTING VERSUS FORECASTING, 353 9.1.2
SEASONAL MODELS INVOLVING ADAPTIVE SINES AND COSINES, 354 9.1.3 GENERAL
MULTIPLICATIVE SEASONAL MODEL, 356 9.2 REPRESENTATION OF THE AIRLINE
DATA BY A MULTIPLICATIVE (0,1, 1) X (0, 1, ) N MODEL, 359 * *- *
9.2.1 MULTIPLICATIVE (0, 1, 1) X(0, 1, ) N MODEL, 359 9.2.2
FORECASTING, 360 9.2.3_ IDENTIFICATION, 367 9.2.4 ESTIMATION, 370 9.2.5
DIAGNOSTIC CHECKING, 375 9.3 SOME ASPECTS OF MORE GENERAL SEASONAL ARIMA
MODELS, 375 9.3.1 MULTIPLICATIVE AND NONMULTIPLICATIVE MODELS, 375 9.3.2
IDENTIFICATION, 379 CONTENTS XV 9.3.3 ESTIMATION, 380 9.3.4 EVENTUAL
FORECAST FUNCTIONS FOR VARIOUS SEASONAL MODELS, 381 9.3.5 CHOICE OF
TRANSFORMATION, 383 9.4 STRUCTURAL COMPONENT MODELS AND DETERMINISTIC
SEASONAL COMPONENTS, 384 9.4.1 O STRUCTURAL COMPONENT TIME SERIES
MODELS, 384 9.4.2 DETERMINISTIC SEASONAL AND TREND COMPONENTS AND COMMON
FACTORS, 388 9.4.3 ESTIMATION OF UNOBSERVED COMPONENTS IN STRUCTURAL
MODELS, 390 9.5 REGRESSION MODELS WITH TIME SERIES ERROR TERMS, 397
9.5.1 MODEL BUILDING, ESTIMATION, AND FORECASTING PROCEDURES FOR
REGRESSION MODELS, 399 9.5.2 RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION
FOR REGRESSION MODELS, 404 A9.1 AUTOCOVARIANCES FOR SOME SEASONAL
MODELS, 407 10 NONLINEAR AND LONG MEMORY MODELS 413 10.1 AUTOREGRESSIVE
CONDITIONAL HETEROSCEDASTIC (ARCH) MODELS, 413 10.1.1 FIRST-ORDER ARCH
MODEL, 415 10.1.2 CONSIDERATION FOR MORE GENERAL MODELS, 416 10.1.3
MODEL BUILDING AND PARAMETER ESTIMATION, 417 10.2 NONLINEAR TIME SERIES
MODELS, 420 10.2.1 CLASSES OF NONLINEAR MODELS, 421 10.2.2 IMPLICATIONS
AND EXAMPLES OF NONLINEAR MODELS, 424 10.3 LONG MEMORY TIME SERIES
PROCESSES, 428 ^- 10.3.1 FRACTIONALLY INTEGRATED PROCESSES, 429 10.3.2
ESTIMATION OF PARAMETERS, 433 PART THREE TRANSFER FUNCTION AND
MULTIVARIATE MODEL BUILDING 437 11 TRANSFER FUNCTION MODELS 439 11.1
LINEAR TRANSFER FUNCTION MODELS, 439 11.1.1 DISCRETE TRANSFER FUNCTION,
439 11.1.2 CONTINUOUS DYNAMIC MODELS REPRESENTED BY DIFFERENTIAL
EQUATIONS, 442 XVI CONTENTS 11.2 DISCRETE DYNAMIC MODELS REPRESENTED BY
DIFFERENCE EQUATIONS, 447 11.2.1 GENERAL FORM OF THE DIFFERENCE
EQUATION, 447 11.2.2 NATURE OF THE TRANSFER FUNCTION, 449 11.2.3 FIRST-
AND SECOND-ORDER DISCRETE TRANSFER FUNCTION MODELS, 450 11.2.4 RECURSIVE
COMPUTATION OF OUTPUT FOR ANY INPUT, 456 11.2.5 TRANSFER FUNCTION MODELS
WITH ADDED NOISE, 458 11.3 RELATION BETWEEN DISCRETE AND CONTINUOUS
MODELS, 458 11.3.1 RESPONSE TO A PULSED INPUT, 459 11.3.2 RELATIONSHIPS
FOR FIRST- AND SECOND-ORDER COINCIDENT SYSTEMS, 461 11.3.3 APPROXIMATING
GENERAL CONTINUOUS MODELS BY DISCRETE MODELS, 464 A 11.1 CONTINUOUS
MODELS WITH PULSED INPUTS, 465 AL 1.2 NONLINEAR TRANSFER FUNCTIONS AND
LINEARIZATION, 470 12 IDENTIFICATION, FITTING, AND CHECKING OF TRANSFER
FUNCTION MODELS 473 12.1 CROSS-CORRELATION FUNCTION, 474 12.1.1
PROPERTIES OF THE CROSS-COVARIANCE AND CROSS-CORRELATION FUNCTIONS, 474
12.1.2 ESTIMATION OF THE CROSS-COVARIANCE AND CROSS-CORRELATION
FUNCTIONS, 477 12.1.3 APPROXIMATE STANDARD ERRORS OF CROSS-CORRELATION
ESTIMATES, 478 12.2 IDENTIFICATION OF TRANSFER FUNCTION MODELS, 481
12.2.1 IDENTIFICATION OF TRANSFER FUNCTION MODELS BY PREWHITENING THE
INPUT, 483 12.2.2 EXAMPLE OF THE IDENTIFICATION OF A TRANSFER FUNCTION
MODEL, 484 *- 12.2.3 IDENTIFICATION OF THE NOISE MODEL, 488 12.2.4
SOME GENERAL CONSIDERATIONS IN IDENTIFYING TRANSFER FUNCTION MODELS, 490
12.3 FITTING AND CHECKING TRANSFER FUNCTION MODELS, 492 12.3.1
CONDITIONAL SUM-OF-SQUARES FUNCTION, 492 12.3.2 NONLINEAR ESTIMATION,
495 12.3.3 USE OF RESIDUALS FOR DIAGNOSTIC CHECKING, 497 12.3.4 SPECIFIC
CHECKS APPLIED TO THE RESIDUALS, 498 12.4 SOME EXAMPLES OF FITTING AND
CHECKING TRANSFER FUNCTION MODELS, 501 CONTENTS XVU 12.4.1 FITTING AND
CHECKING OF THE GAS FURNACE MODEL, 501 12.4.2 SIMULATED EXAMPLE WITH TWO
INPUTS, 507 12.5 FORECASTING WITH TRANSFER FUNCTION MODELS USING LEADING
INDICATORS, 509 12.5.1 MINIMUM MEAN SQUARE ERROR FORECAST, 510 12.5.2
FORECAST OF CO2 OUTPUT FROM GAS FURNACE, 514 12.5.3 FORECAST OF
NONSTATIONARY SALES DATA USING A LEADING INDICATOR, 517 12.6 SOME
ASPECTS OF THE DESIGN OF EXPERIMENTS TO ESTIMATE TRANSFER FUNCTIONS, 519
A 12.1 USE OF CROSS SPECTRAL ANALYSIS FOR TRANSFER FUNCTION MODEL
IDENTIFICATION, 521 A12.1.1 IDENTIFICATION OF SINGLE INPUT TRANSFER
FUNCTION MODELS, 521 A12.1.2 IDENTIFICATION OF MULTIPLE INPUT TRANSFER
FUNCTION MODELS, 523 A 12.2 CHOICE OF INPUT TO PROVIDE OPTIMAL PARAMETER
ESTIMATES, 524 A12.2.1 DESIGN OF OPTIMAL INPUTS FOR A SIMPLE SYSTEM, 524
A 12.2.2 NUMERICAL EXAMPLE, 527 13 INTERVENTION ANALYSIS MODELS AND
OUTLIER DETECTION 529 13.1 INTERVENTION ANALYSIS METHODS, 529 13.1.1
MODELS FOR INTERVENTION ANALYSIS, 529 13.1.2 EXAMPLE OF INTERVENTION
ANALYSIS, 532 13.1.3 NATURE OF THE MLE FOR A SIMPLE LEVEL CHANGE
PARAMETER MODEL, 533 ^..**** 13.2 OUTLIER ANALYSIS FOR TIME SERIES, 536
.- ~^ 13.2.1 MODELS FOR ADDITIVE AND INNOVATIONAL OUTLIERS, 537
13.2.2 ESTIMATION OF OUTLIER EFFECT FOR KNOWN TIMING OF THE OUTLIER, 538
13.2.3 ITERATIVE PROCEDURE FOR OUTLIER DETECTION, 540 13.2.4 EXAMPLES OF
ANALYSIS OF OUTLIERS, 541 13.3 ESTIMATION FOR ARMA MODELS WITH MISSING
VALUES, 543 13.3.1 STATE-SPACE MODEL AND KALMAN FILTER WITH MISSING
VALUES, 544 13.3.2 ESTIMATION OF MISSING VALUES OF AN ARMA PROCESS, 546
CONTENTS 14 MULTIVARIATE TIME SERIES ANALYSIS 551 14.1 STATIONARY
MULTIVARIATE TIME SERIES, 552 14.1.1 COVARIANCE PROPERTIES OF STATIONARY
MULTIVARIATE TIME SERIES, 552 14.1.2 SPECTRAL CHARACTERISTICS FOR
STATIONARY MULTIVARIATE PROCESSES, 554 14.1.3 LINEAR FILTERING RELATIONS
FOR STATIONARY MULTIVARIATE PROCESSES, 555 14.2 LINEAR MODEL
REPRESENTATIONS FOR STATIONARY MULTIVARIATE PROCESSES, 556 14.2.1 VECTOR
AUTOREGRESSIVE-MOVING AVERAGE (ARMA) MODELS AND REPRESENTATIONS, 557
14.2.2 ASPECTS OF NONUNIQUENESS AND PARAMETER IDENTIFIABILITY FOR VECTOR
ARMA MODELS, 563 14.2.3 ECHELON CANONICAL FORM OF THE VECTOR ARMA MODEL,
565 14.2.4 RELATION OF VECTOR ARMA TO TRANSFER FUNCTION AND ARMAX MODEL
FORMS, 569 14.3 NONSTATIONARY VECTOR AUTOREGRESSIVE-MOVING AVERAGE
MODELS, 570 14.4 FORECASTING FOR VECTOR AUTOREGRESSIVE-MOVING AVERAGE
PROCESSES, 573 14.4.1 CALCULATION OF FORECASTS FROM ARMA DIFFERENCE
EQUATION, 573 14.4.2 FORECASTS FROM INFINITE MA FORM AND PROPERTIES OF
FORECAST ERRORS, 575 14.5 STATE-SPACE FORM OF THE VECTOR ARMA MODEL, 575
14.6 STATISTICAL ANALYSIS OF VECTOR ARMA MODELS, 578 14.6.1 INITIAL
MODEL BUILDING AND LEAST SQUARES FOR VECTOR AR MODELS, 578 14.6.2
ESTIMATION AND MODEL CHECKING FOR VECTOR ARMA MODELS, 583 14.6.3
ESTIMATION AND INFERENCES FOR CO-INTEGRATED VECTOR AR MODELS, 585 14.7
EXAMPLE OF VECTOR ARMA MODELING, 588 PART FOUR DESIGN OF DISCRETE
CONTROL SCHEMES 597 15 ASPECTS OF PROCESS CONTROL 599 15.1 PROCESS
MONITORING AND PROCESS ADJUSTMENT, 600 15.1.1 PROCESS MONITORING, 600
CONTENTS XIX 15.1.2 PROCESS ADJUSTMENT, 603 15.2 PROCESS ADJUSTMENT
USING FEEDBACK CONTROL, 604 15.2.1 FEEDBACK ADJUSTMENT CHART, 605 15.2.2
MODELING THE FEEDBACK LOOP, 607 15.2.3 SIMPLE MODELS FOR DISTURBANCES
AND DYNAMICS, 608 15.2.4 GENERAL MINIMUM MEAN SQUARE ERROR FEEDBACK
CONTROL SCHEMES, 612 15.2.5 MANUAL ADJUSTMENT FOR DISCRETE
PROPORTIONAL-INTEGRAL SCHEMES, 615 15.2.6 COMPLEMENTARY ROLES OF
MONITORING AND ADJUSTMENT, 617 15.3 EXCESSIVE ADJUSTMENT SOMETIMES
REQUIRED BY MMSE CONTROL, 620 15.3.1 CONSTRAINED CONTROL, 621 15.4
MINIMUM COST CONTROL WITH FIXED COSTS OF ADJUSTMENT AND MONITORING, 623
15.4.1 BOUNDED ADJUSTMENT SCHEME FOR FIXED ADJUSTMENT COST, 623 15.4.2
INDIRECT APPROACH FOR OBTAINING A BOUNDED ADJUSTMENT SCHEME, 625 15.4.3
INCLUSION OF THE COST OF MONITORING, 627 15.5 FEEDFORWARD CONTROL, 627
15.5.1 FEEDFORWARD CONTROL TO MINIMIZE MEAN SQUARE ERROR AT THE OUTPUT,
629 15.5.2 AN EXAMPLE*CONTROL OF THE SPECIFIC GRAVITY OF AN INTERMEDIATE
PRODUCT, 632 15.5.3 FEEDFORWARD CONTROL WITH MULTIPLE INPUTS, 635 15.5.4
FEEDFORWARD-FEEDBACK CONTROL, 636 15.5.5 ADVANTAGES AND DISADVANTAGES OF
FEEDFORWARD AND FEEDBACK CONTROL, 638 -* ^ 15.5.6 REMARKS ON FITTING
TRANSFER FUNCTION-NOISE MODELS USING OPERATING DATA, 639 15.6 MONITORING
VALUES OF PARAMETERS OF FORECASTING AND FEEDBACK ADJUSTMENT SCHEMES, 642
A 15.1 FEEDBACK CONTROL SCHEMES WHERE THE ADJUSTMENT VARIANCE IS
RESTRICTED, 644 [ A15.1.1 DERIVATION OF OPTIMAL ADJUSTMENT, 644 A15.2
CHOICE OF THE SAMPLING INTERVAL, 653 A15.2.1 ILLUSTRATION OF THE EFFECT
OF REDUCING SAMPLING FREQUENCY, 654 A 15.2.2 SAMPLING AN IMA(0, 1,1)
PROCESS, 654 XX CONTENTS PART FIVE CHARTS AND TABLES 659 COLLECTION OF
TABLES AND CHARTS 661 COLLECTION OF TIME SERIES USED FOR EXAMPLES IN THE
TEXT AND IN EXERCISES 669 REFERENCES 685 PART SIX EXERCISES AND PROBLEMS
701 INDEX 729
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1 TIME SERIES ANALYSIS FORECASTING AND GONTROL FOURTH EDITION GEORGE E.
P. BOX GWILYM M. JENKINS GREGORY C. REINSEL WILEY A JOHN WILEY & SONS,
INC., PUBLICATION CONTENTS PREFACE TO THE FOURTH EDITION XXI PREFACE TO
THE THIRD EDITION XXIII 1 INTRODUCTION 1 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, 5
1.1.5 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, 17 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 VII VIII CONTENTS 2.1.3 POSITIVE
DEFINITENESS AND THE AUTOCOVARIANCE MATRIX, 25 2.1.4 AUTOCOVARIANCE AND
AUTOCORRELATION FUNCTIONS, 29 2.1.5 ESTIMATION OF AUTOCOVARIANCE AND
AUTOCORRELATION FUNCTIONS, 31 2.1.6 STANDARD ERRORS OF AUTOCORRELATION
ESTIMATES, 33 2.2 SPECTRAL PROPERTIES OF STATIONARY MODELS, 35 2.2.1
PERIODOGRAM OF A TIME SERIES, 35 2.2.2 ANALYSIS OF VARIANCE, 37 2.2.3
SPECTRUM AND SPECTRAL DENSITY FUNCTION, 38 2.2.4 SIMPLE EXAMPLES OF
AUTOCORRELATION AND SPECTRAL DENSITY FUNCTIONS, 43 2.2.5 ADVANTAGES AND
DISADVANTAGES OF THE AUTOCORRELATION AND SPECTRAL DENSITY FUNCTIONS, 45
A2.1 LINK BETWEEN THE SAMPLE SPECTRUM AND AUTOCOVARIANCE FUNCTION
ESTIMATE, 45 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, 53 3.2 AUTOREGRESSIVE
PROCESSES, 55 3.2.1 STATIONARITY CONDITIONS FOR AUTOREGRESSIVE
PROCESSES, 55 3.2.2 AUTOCORRELATION FUNCTION AND SPECTRUM OF
AUTOREGRESSIVE PROCESSES, 57 3.2.3 FIRST-ORDER AUTOREGRESSIVE (MARKOV)
PROCESS, 59 3.2.4 SECOND-ORDER AUTOREGRESSIVE PROCESS, 61 3.2.5 PARTIAL
AUTOCORRELATION FUNCTION, 66 3.2.6 ESTIMATION OF THE PARTIAL
AUTOCORRELATION FUNCTION, 69 3.2.7 STANDARD ERRORS OF PARTIAL
AUTOCORRELATION ESTIMATES, 70 3.3 MOVING AVERAGE PROCESSES, 71 CONTENTS
IX 3.3.1 INVERTIBILITY CONDITIONS FOR MOVING AVERAGE PROCESSES, 71 3.3.2
AUTOCORRELATION FUNCTION AND SPECTRUM OF MOVING AVERAGE PROCESSES, 72
3.3.3 FIRST-ORDER MOVING AVERAGE PROCESS, 73 3.3.4 SECOND-ORDER MOVING
AVERAGE PROCESS, 75 3.3.5 DUALITY BETWEEN AUTOREGRESSIVE AND MOVING
AVERAGE PROCESSES, 78 3.4 MIXED AUTOREGRESSIVE-MOVING AVERAGE PROCESSES,
79 3.4.1 STATIONARITY AND INVERTIBILITY PROPERTIES, 79 3.4.2
AUTOCORRELATION FUNCTION AND SPECTRUM OF MIXED PROCESSES, 80 3.4.3
FIRST-ORDER AUTOREGRESSIVE-FIRST-ORDER MOVING AVERAGE PROCESS, 82 3.4.4
SUMMARY, 86 A3.1 AUTOCOVARIANCES, AUTOCOVARIANCE GENERATING FUNCTION,
AND STATIONARITY CONDITIONS FOR A GENERAL LINEAR PROCESS, 86 A3.2
RECURSIVE METHOD FOR CALCULATING ESTIMATES OF AUTOREGRESSIVE PARAMETERS,
89 4 LINEAR NONSTATIONARY MODELS 4.1 AUTOREGRESSIVE INTEGRATED MOVING
AVERAGE PROCESSES, 93 4.1.1 NONSTATIONARY FIRST-ORDER AUTOREGRESSIVE
PROCESS, 93 4.1.2 GENERAL MODEL FOR A NONSTATIONARY PROCESS EXHIBITING
HOMOGENEITY, 95 4.1.3 GENERAL FORM OF THE AUTOREGRESSIVE INTEGRATED
MOVING AVERAGE MODEL, 100 4.2 THREE EXPLICIT FORMS FOR THE
AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL, 103 . -' 4.2.1
DIFFERENCE EQUATION FORM OF THE MODEC 103 4.2.2 RANDOM SHOCK FORM OF THE
MODEL, 104 4.2.3 INVERTED FORM OF THE MODEL, 111 4.3 INTEGRATED MOVING
AVERAGE PROCESSES, 114 4.3.1 INTEGRATED MOVING AVERAGE PROCESS OF ORDER
(0, 1, 1), 115 4.3.2 INTEGRATED MOVING AVERAGE PROCESS OF ORDER (0, 2,
2), 119 4.3.3 GENERAL INTEGRATED MOVING AVERAGE PROCESS OF ORDER (0, D,
Q), 123 A4.1 LINEAR DIFFERENCE EQUATIONS, 125 A4.2 IMA(0, 1,1) PROCESS
WITH DETERMINISTIC DRIFT, 131 93 K CONTENTS A4.3 ARIMA PROCESSES WITH
ADDED NOISE, 131 A4.3.1 SUM OF TWO INDEPENDENT MOVING AVERAGE PROCESSES,
132 A4.3.2 EFFECT OF ADDED NOISE ON THE GENERAL MODEL, 133 A4.3.3
EXAMPLE FOR AN IMA(0, 1, 1) PROCESS WITH ADDED WHITE NOISE, 134 A4.3.4
RELATION BETWEEN THE IMA(0, 1,1) PROCESS AND A RANDOM WALK, 135 A4.3.5
AUTOCOVARIANCE FUNCTION OF THE GENERAL MODEL WITH ADDED CORRELATED
NOISE, 135 5 FORECASTING 137 5.1 MINIMUM MEAN SQUARE ERROR FORECASTS AND
THEIR PROPERTIES, 137 5.1.1 DERIVATION OF THE MINIMUM MEAN SQUARE ERROR
FORECASTS, 139 5.1.2 THREE BASIC FORMS FOR THE FORECAST, 141 5.2
CALCULATING AND UPDATING FORECASTS, 145 5.2.1 CONVENIENT FORMAT FOR THE
FORECASTS, 145 5.2.2 CALCULATION OF THE ^ WEIGHTS, 147 5.2.3 USE OF THE
\JR WEIGHTS IN UPDATING THE FORECASTS, 148 5.2.4 CALCULATION OF THE
PROBABILITY LIMITS OF THE FORECASTS AT ANY LEAD TIME, 150 5.3 FORECAST
FUNCTION AND FORECAST WEIGHTS, 152 5.3.1 EVENTUAL FORECAST FUNCTION
DETERMINED BY THE AUTOREGRESSIVE OPERATOR, 152 5.3.2 ROLE OF THE MOVING
AVERAGE OPERATOR IN FIXING THE INITIAL VALUES, 153 5.3.3 LEAD / FORECAST
WEIGHTS, 154 5.4 EXAMPLES OF FORECAST FUNCTIONS AND THEIR UPDATING, 157
5.4.1 FORECASTING AN IMA(0, 1, 1) PROCESS, 157 5.4.2 FORECASTING AN
IMA(0, 2, 2) PROCESS, 160 5.4.3 FORECASTING A GENERAL IMA(0, D, Q)
PROCESS, 163 5.4.4 FORECASTING AUTOREGRESSIVE PROCESSES, 164 5.4.5
FORECASTING A (1, 0, 1) PROCESS, 167 5.4.6 FORECASTING A (1, 1, 1)
PROCESS, 169 T CONTENTS XI 5.5 USE OF STATE-SPACE MODEL FORMULATION FOR
EXACT FORECASTING, 170 5.5.1 STATE-SPACE MODEL REPRESENTATION FOR THE
ARIMA PROCESS, 170 5.5.2 KALMAN FILTERING RELATIONS FOR USE IN
PREDICTION, 171 5.5.3 SMOOTHING RELATIONS IN THE STATE VARIABLE MODEL,
175 5.6 SUMMARY, 177 A5.1 CORRELATIONS BETWEEN FORECAST ERRORS, 180
A5.1.1 AUTOCORRELATION FUNCTION OF FORECAST ERRORS AT DIFFERENT ORIGINS,
180 A5.1.2 CORRELATION BETWEEN FORECAST ERRORS AT THE SAME ORIGIN WITH
DIFFERENT LEAD TIMES, 182 A5.2 FORECAST WEIGHTS FOR ANY LEAD TIME, 182
A5.3 FORECASTING IN TERMS OF THE GENERAL INTEGRATED FORM, 185 A5.3.1
GENERAL METHOD OF OBTAINING THE INTEGRATED FORM, 185 A5.3.2 UPDATING THE
GENERAL INTEGRATED FORM, 187 A5.3.3 COMPARISON WITH THE DISCOUNTED LEAST
SQUARES METHOD, 187 PART TWO STOCHASTIC MODEL BUILDING 193 6 MODEL
IDENTIFICATION 195 6.1 OBJECTIVES OF IDENTIFICATION, 195 6.1.1 STAGES IN
THE IDENTIFICATION PROCEDURE, 195 6.2 IDENTIFICATION TECHNIQUES, 196
6.2.1 USE OF THE AUTOCORRELATION AND PARTIAJL^.^ AUTOCORRELATION
FUNCTIONS IN IDENTIFICATION, 196 6.2.2 STANDARD ERRORS FOR ESTIMATED
AUTOCORRELATIONS AND PARTIAL AUTOCORRELATIONS, 198 6.2.3 IDENTIFICATION
OF SOME ACTUAL TIME SERIES, 200 6.2.4 SOME ADDITIONAL MODEL
IDENTIFICATION TOOLS, 208 6.3 INITIAL ESTIMATES FOR THE PARAMETERS, 213
6.3.1 UNIQUENESS OF ESTIMATES OBTAINED FROM THE AUTOCOVARIANCE FUNCTION,
213 6.3.2 INITIAL ESTIMATES FOR MOVING AVERAGE PROCESSES, 213 6.3.3
INITIAL ESTIMATES FOR AUTOREGRESSIVE PROCESSES, 215 XII CONTENTS 6.3.4
INITIAL ESTIMATES FOR MIXED AUTOREGRESSIVE-MOVING AVERAGE PROCESSES, 216
6.3.5 INITIAL ESTIMATE OF ERROR VARIANCE, 218 6.3.6 APPROXIMATE STANDARD
ERROR FOR W, 218 6.3.7 CHOICE BETWEEN STATIONARY AND NONSTATIONARY
MODELS IN DOUBTFUL CASES, 220 6.4 MODEL MULTIPLICITY, 221 6.4.1
MULTIPLICITY OF AUTOREGRESSIVE-MOVING AVERAGE MODELS, 221 6.4.2 MULTIPLE
MOMENT SOLUTIONS FOR MOVING AVERAGE PARAMETERS, 224 6.4.3 USE OF THE
BACKWARD PROCESS TO DETERMINE STARTING VALUES, 225 A6.1 EXPECTED
BEHAVIOR OF THE ESTIMATED AUTOCORRELATION FUNCTION FOR A NONSTATIONARY
PROCESS, 225 A6.2 GENERAL METHOD FOR OBTAINING INITIAL ESTIMATES OF THE
PARAMETERS OF A MIXED AUTOREGRESSIVE-MOVING AVERAGE PROCESS, 226 7 MODEL
ESTIMATION 231 7.1 STUDY OF THE LIKELIHOOD AND SUM-OF-SQUARES FUNCTIONS,
231 7.1.1 LIKELIHOOD FUNCTION, 231 7.1.2 CONDITIONAL LIKELIHOOD FOR AN
ARIMA PROCESS, 232 7.1.3 CHOICE OF STARTING VALUES FOR CONDITIONAL
CALCULATION, 234 7.1.4 UNCONDITIONAL LIKELIHOOD; SUM-OF-SQUARES
FUNCTION; LEAST SQUARES ESTIMATES, 235 7.1.5 GENERAL PROCEDURE FOR
CALCULATING THE UNCONDITIONAL SUM OF SQUARES, 240 ' 7.1.6 GRAPHICAL
STUDY OF THE SUM-OF-SQUARES FUNCTION, 245 7.1.7 DESCRIPTION OF
"WELL-BEHAVED" ESTIMATION SITUATIONS; CONFIDENCE REGIONS, 248 7.2
NONLINEAR ESTIMATION, 255 7.2.1 GENERAL METHOD OF APPROACH, 255 7.2.2
NUMERICAL ESTIMATES OF THE DERIVATIVES, 257 7.2.3 DIRECT EVALUATION OF
THE DERIVATIVES, 258 7.2.4 GENERAL LEAST SQUARES ALGORITHM FOR THE
CONDITIONAL MODEL, 260 7.2.5 SUMMARY OF MODELS FITTED TO SERIES A TO F,
263 CONTENTS XIII 7.2.6 LARGE-SAMPLE INFORMATION MATRICES AND COVARIANCE
ESTIMATES, 264 7.3 SOME ESTIMATION RESULTS FOR SPECIFIC MODELS, 268
7.3.1 AUTOREGRESSIVE PROCESSES, 268 7.3.2 MOVING AVERAGE PROCESSES, 270
7.3.3 MIXED PROCESSES, 271 7.3.4 SEPARATION OF LINEAR AND NONLINEAR
COMPONENTS IN ESTIMATION, 271 7.3.5 PARAMETER REDUNDANCY, 273 7.4
LIKELIHOOD FUNCTION BASED ON THE STATE-SPACE MODEL, 275 7.5 UNIT ROOTS
IN ARIMA MODELS, 280 7.5.1 FORMAL TESTS FOR UNIT ROOTS IN AR MODELS, 281
7.5.2 EXTENSIONS OF UNIT-ROOT TESTING TO MIXED ARIMA MODELS, 286 7.6
ESTIMATION USING BAYES'S THEOREM, 287 7.6.1 BAYES'S THEOREM, 287 7.6.2
BAYESIAN ESTIMATION OF PARAMETERS, 289 7.6.3 AUTOREGRESSIVE PROCESSES,
290 7.6.4 MOVING AVERAGE PROCESSES, 293 7.6.5 MIXED PROCESSES, 294 A7.1
REVIEW OF NORMAL DISTRIBUTION THEORY, 296 A7.1.1 PARTITIONING OF A
POSITIVE-DEFINITE QUADRATIC FORM, 296 A7.1.2 TWO USEFUL INTEGRALS, 296
A7.1.3 NORMAL DISTRIBUTION, 297 A7.1.4 STUDENT'S T DISTRIBUTION, 300
A7.2 REVIEW OF LINEAR LEAST SQUARES THEORY, 303 A7.2.1 NORMAL EQUATIONS
AND LEAST SQUARES, 303^ HI.2.2 ESTIMATION OF ERROR VARIANCE, 3OT A7.2.3
COVARIANCE MATRIX OF LEAST SQUARES ESTIMATES, 305 A7.2.4 CONFIDENCE
REGIONS, 305 A7.2.5 CORRELATED ERRORS, 305 A7.3 EXACT LIKELIHOOD
FUNCTION FOR MOVING AVERAGE AND MIXED PROCESSES, 306 A7.4 EXACT
LIKELIHOOD FUNCTION FOR AN AUTOREGRESSIVE PROCESS, 314 A7.5 ASYMPTOTIC
DISTRIBUTION OF ESTIMATORS FOR AUTOREGRESSIVE MODELS, 323 XIV CONTENTS
A7.6 EXAMPLES OF THE EFFECT OF PARAMETER ESTIMATION ERRORS ON VARIANCES
OF FORECAST ERRORS AND PROBABILITY LIMITS FOR FORECASTS, 327 A7.7
SPECIAL NOTE ON ESTIMATION OF MOVING AVERAGE PARAMETERS, 330 8 MODEL
DIAGNOSTIC CHECKING 333 8.1 CHECKING THE STOCHASTIC MODEL, 333 8.1.1
GENERAL PHILOSOPHY, 333 8.1.2 OVERFITTING, 334 8.2 DIAGNOSTIC CHECKS
APPLIED TO RESIDUALS, 335 8.2.1 AUTOCORRELATION CHECK, 337 8.2.2
PORTMANTEAU LACK-OF-FIT TEST, 338 8.2.3 MODEL INADEQUACY ARISING FROM
CHANGES IN PARAMETER VALUES, 343 8.2.4 SCORE TESTS FOR MODEL CHECKING,
344 8.2.5 CUMULATIVE PERIODOGRAM CHECK, 347 8.3 USE OF RESIDUALS TO
MODIFY THE MODEL, 350 8.3.1 NATURE OF THE CORRELATIONS IN THE RESIDUALS
WHEN AN INCORRECT MODEL IS USED, 350 8.3.2 USE OF RESIDUALS TO MODIFY
THE MODEL, 352 9 SEASONAL MODELS 353 9.1 PARSIMONIOUS MODELS FOR
SEASONAL TIME SERIES, 353 9.1.1 FITTING VERSUS FORECASTING, 353 9.1.2
SEASONAL MODELS INVOLVING ADAPTIVE SINES AND COSINES, 354 9.1.3 GENERAL
MULTIPLICATIVE SEASONAL MODEL, 356 9.2 REPRESENTATION OF THE AIRLINE
DATA BY A MULTIPLICATIVE (0,1, 1) X (0, 1, \) N MODEL, 359 * *-"*""
9.2.1 MULTIPLICATIVE (0, 1, 1) X(0, 1, \) N MODEL, 359 9.2.2
FORECASTING, 360 9.2.3_ IDENTIFICATION, 367 9.2.4 ESTIMATION, 370 9.2.5
DIAGNOSTIC CHECKING, 375 9.3 SOME ASPECTS OF MORE GENERAL SEASONAL ARIMA
MODELS, 375 9.3.1 MULTIPLICATIVE AND NONMULTIPLICATIVE MODELS, 375 9.3.2
IDENTIFICATION, 379 CONTENTS XV 9.3.3 ESTIMATION, 380 9.3.4 EVENTUAL
FORECAST FUNCTIONS FOR VARIOUS SEASONAL MODELS, 381 9.3.5 CHOICE OF
TRANSFORMATION, 383 9.4 STRUCTURAL COMPONENT MODELS AND DETERMINISTIC
SEASONAL COMPONENTS, 384 9.4.1 O STRUCTURAL COMPONENT TIME SERIES
MODELS, 384 9.4.2 DETERMINISTIC SEASONAL AND TREND COMPONENTS AND COMMON
FACTORS, 388 9.4.3 ESTIMATION OF UNOBSERVED COMPONENTS IN STRUCTURAL
MODELS, 390 9.5 REGRESSION MODELS WITH TIME SERIES ERROR TERMS, 397
9.5.1 MODEL BUILDING, ESTIMATION, AND FORECASTING PROCEDURES FOR
REGRESSION MODELS, 399 9.5.2 RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION
FOR REGRESSION MODELS, 404 A9.1 AUTOCOVARIANCES FOR SOME SEASONAL
MODELS, 407 10 NONLINEAR AND LONG MEMORY MODELS 413 10.1 AUTOREGRESSIVE
CONDITIONAL HETEROSCEDASTIC (ARCH) MODELS, 413 10.1.1 FIRST-ORDER ARCH
MODEL, 415 10.1.2 CONSIDERATION FOR MORE GENERAL MODELS, 416 10.1.3
MODEL BUILDING AND PARAMETER ESTIMATION, 417 10.2 NONLINEAR TIME SERIES
MODELS, 420 10.2.1 CLASSES OF NONLINEAR MODELS, 421 10.2.2 IMPLICATIONS
AND EXAMPLES OF NONLINEAR MODELS, 424 10.3 LONG MEMORY TIME SERIES
PROCESSES, 428 ^-' 10.3.1 FRACTIONALLY INTEGRATED PROCESSES, 429" 10.3.2
ESTIMATION OF PARAMETERS, 433 PART THREE TRANSFER FUNCTION AND
MULTIVARIATE MODEL BUILDING 437 11 TRANSFER FUNCTION MODELS 439 11.1
LINEAR TRANSFER FUNCTION MODELS, 439 11.1.1 DISCRETE TRANSFER FUNCTION,
439 11.1.2 CONTINUOUS DYNAMIC MODELS REPRESENTED BY DIFFERENTIAL
EQUATIONS, 442 XVI CONTENTS 11.2 DISCRETE DYNAMIC MODELS REPRESENTED BY
DIFFERENCE EQUATIONS, 447 11.2.1 GENERAL FORM OF THE DIFFERENCE
EQUATION, 447 11.2.2 NATURE OF THE TRANSFER FUNCTION, 449 11.2.3 FIRST-
AND SECOND-ORDER DISCRETE TRANSFER FUNCTION MODELS, 450 11.2.4 RECURSIVE
COMPUTATION OF OUTPUT FOR ANY INPUT, 456 11.2.5 TRANSFER FUNCTION MODELS
WITH ADDED NOISE, 458 11.3 RELATION BETWEEN DISCRETE AND CONTINUOUS
MODELS, 458 11.3.1 RESPONSE TO A PULSED INPUT, 459 11.3.2 RELATIONSHIPS
FOR FIRST- AND SECOND-ORDER COINCIDENT SYSTEMS, 461 11.3.3 APPROXIMATING
GENERAL CONTINUOUS MODELS BY DISCRETE MODELS, 464 A 11.1 CONTINUOUS
MODELS WITH PULSED INPUTS, 465 AL 1.2 NONLINEAR TRANSFER FUNCTIONS AND
LINEARIZATION, 470 12 IDENTIFICATION, FITTING, AND CHECKING OF TRANSFER
FUNCTION MODELS 473 12.1 CROSS-CORRELATION FUNCTION, 474 12.1.1
PROPERTIES OF THE CROSS-COVARIANCE AND CROSS-CORRELATION FUNCTIONS, 474
12.1.2 ESTIMATION OF THE CROSS-COVARIANCE AND CROSS-CORRELATION
FUNCTIONS, 477 12.1.3 APPROXIMATE STANDARD ERRORS OF CROSS-CORRELATION
ESTIMATES, 478 12.2 IDENTIFICATION OF TRANSFER FUNCTION MODELS, 481
12.2.1 IDENTIFICATION OF TRANSFER FUNCTION MODELS BY PREWHITENING THE
INPUT, 483 12.2.2 EXAMPLE OF THE IDENTIFICATION OF A TRANSFER FUNCTION
MODEL, 484 *- " " 12.2.3 IDENTIFICATION OF THE NOISE MODEL, 488 12.2.4
SOME GENERAL CONSIDERATIONS IN IDENTIFYING TRANSFER FUNCTION MODELS, 490
12.3 FITTING AND CHECKING TRANSFER FUNCTION MODELS, 492 12.3.1
CONDITIONAL SUM-OF-SQUARES FUNCTION, 492 12.3.2 NONLINEAR ESTIMATION,
495 12.3.3 USE OF RESIDUALS FOR DIAGNOSTIC CHECKING, 497 12.3.4 SPECIFIC
CHECKS APPLIED TO THE RESIDUALS, 498 12.4 SOME EXAMPLES OF FITTING AND
CHECKING TRANSFER FUNCTION MODELS, 501 CONTENTS XVU 12.4.1 FITTING AND
CHECKING OF THE GAS FURNACE MODEL, 501 12.4.2 SIMULATED EXAMPLE WITH TWO
INPUTS, 507 12.5 FORECASTING WITH TRANSFER FUNCTION MODELS USING LEADING
INDICATORS, 509 12.5.1 MINIMUM MEAN SQUARE ERROR FORECAST, 510 12.5.2
FORECAST OF CO2 OUTPUT FROM GAS FURNACE, 514 12.5.3 FORECAST OF
NONSTATIONARY SALES DATA USING A LEADING INDICATOR, 517 12.6 SOME
ASPECTS OF THE DESIGN OF EXPERIMENTS TO ESTIMATE TRANSFER FUNCTIONS, 519
A 12.1 USE OF CROSS SPECTRAL ANALYSIS FOR TRANSFER FUNCTION MODEL
IDENTIFICATION, 521 A12.1.1 IDENTIFICATION OF SINGLE INPUT TRANSFER
FUNCTION MODELS, 521 A12.1.2 IDENTIFICATION OF MULTIPLE INPUT TRANSFER
FUNCTION MODELS, 523 A 12.2 CHOICE OF INPUT TO PROVIDE OPTIMAL PARAMETER
ESTIMATES, 524 A12.2.1 DESIGN OF OPTIMAL INPUTS FOR A SIMPLE SYSTEM, 524
A 12.2.2 NUMERICAL EXAMPLE, 527 13 INTERVENTION ANALYSIS MODELS AND
OUTLIER DETECTION 529 13.1 INTERVENTION ANALYSIS METHODS, 529 13.1.1
MODELS FOR INTERVENTION ANALYSIS, 529 13.1.2 EXAMPLE OF INTERVENTION
ANALYSIS, 532 13.1.3 NATURE OF THE MLE FOR A SIMPLE LEVEL CHANGE
PARAMETER MODEL, 533 ^.****" 13.2 OUTLIER ANALYSIS FOR TIME SERIES, 536
.- ~^" 13.2.1 MODELS FOR ADDITIVE AND INNOVATIONAL OUTLIERS, 537
13.2.2 ESTIMATION OF OUTLIER EFFECT FOR KNOWN TIMING OF THE OUTLIER, 538
13.2.3 ITERATIVE PROCEDURE FOR OUTLIER DETECTION, 540 13.2.4 EXAMPLES OF
ANALYSIS OF OUTLIERS, 541 13.3 ESTIMATION FOR ARMA MODELS WITH MISSING
VALUES, 543 13.3.1 STATE-SPACE MODEL AND KALMAN FILTER WITH MISSING
VALUES, 544 13.3.2 ESTIMATION OF MISSING VALUES OF AN ARMA PROCESS, 546
CONTENTS 14 MULTIVARIATE TIME SERIES ANALYSIS 551 14.1 STATIONARY
MULTIVARIATE TIME SERIES, 552 14.1.1 COVARIANCE PROPERTIES OF STATIONARY
MULTIVARIATE TIME SERIES, 552 14.1.2 SPECTRAL CHARACTERISTICS FOR
STATIONARY MULTIVARIATE PROCESSES, 554 14.1.3 LINEAR FILTERING RELATIONS
FOR STATIONARY MULTIVARIATE PROCESSES, 555 14.2 LINEAR MODEL
REPRESENTATIONS FOR STATIONARY MULTIVARIATE PROCESSES, 556 14.2.1 VECTOR
AUTOREGRESSIVE-MOVING AVERAGE (ARMA) MODELS AND REPRESENTATIONS, 557
14.2.2 ASPECTS OF NONUNIQUENESS AND PARAMETER IDENTIFIABILITY FOR VECTOR
ARMA MODELS, 563 14.2.3 ECHELON CANONICAL FORM OF THE VECTOR ARMA MODEL,
565 14.2.4 RELATION OF VECTOR ARMA TO TRANSFER FUNCTION AND ARMAX MODEL
FORMS, 569 14.3 NONSTATIONARY VECTOR AUTOREGRESSIVE-MOVING AVERAGE
MODELS, 570 14.4 FORECASTING FOR VECTOR AUTOREGRESSIVE-MOVING AVERAGE
PROCESSES, 573 14.4.1 CALCULATION OF FORECASTS FROM ARMA DIFFERENCE
EQUATION, 573 14.4.2 FORECASTS FROM INFINITE MA FORM AND PROPERTIES OF
FORECAST ERRORS, 575 14.5 STATE-SPACE FORM OF THE VECTOR ARMA MODEL, 575
14.6 STATISTICAL ANALYSIS OF VECTOR ARMA MODELS, 578 14.6.1 INITIAL
MODEL BUILDING AND LEAST SQUARES FOR VECTOR AR MODELS, 578 14.6.2
ESTIMATION AND MODEL CHECKING FOR VECTOR ARMA MODELS, 583 14.6.3
ESTIMATION AND INFERENCES FOR CO-INTEGRATED VECTOR AR MODELS, 585 14.7
EXAMPLE OF VECTOR ARMA MODELING, 588 PART FOUR DESIGN OF DISCRETE
CONTROL SCHEMES 597 15 ASPECTS OF PROCESS CONTROL 599 15.1 PROCESS
MONITORING AND PROCESS ADJUSTMENT, 600 15.1.1 PROCESS MONITORING, 600
CONTENTS XIX 15.1.2 PROCESS ADJUSTMENT, 603 15.2 PROCESS ADJUSTMENT
USING FEEDBACK CONTROL, 604 15.2.1 FEEDBACK ADJUSTMENT CHART, 605 15.2.2
MODELING THE FEEDBACK LOOP, 607 15.2.3 SIMPLE MODELS FOR DISTURBANCES
AND DYNAMICS, 608 15.2.4 GENERAL MINIMUM MEAN SQUARE ERROR FEEDBACK
CONTROL SCHEMES, 612 15.2.5 MANUAL ADJUSTMENT FOR DISCRETE
PROPORTIONAL-INTEGRAL SCHEMES, 615 15.2.6 COMPLEMENTARY ROLES OF
MONITORING AND ADJUSTMENT, 617 15.3 EXCESSIVE ADJUSTMENT SOMETIMES
REQUIRED BY MMSE CONTROL, 620 15.3.1 CONSTRAINED CONTROL, 621 15.4
MINIMUM COST CONTROL WITH FIXED COSTS OF ADJUSTMENT AND MONITORING, 623
15.4.1 BOUNDED ADJUSTMENT SCHEME FOR FIXED ADJUSTMENT COST, 623 15.4.2
INDIRECT APPROACH FOR OBTAINING A BOUNDED ADJUSTMENT SCHEME, 625 15.4.3
INCLUSION OF THE COST OF MONITORING, 627 15.5 FEEDFORWARD CONTROL, 627
15.5.1 FEEDFORWARD CONTROL TO MINIMIZE MEAN SQUARE ERROR AT THE OUTPUT,
629 15.5.2 AN EXAMPLE*CONTROL OF THE SPECIFIC GRAVITY OF AN INTERMEDIATE
PRODUCT, 632 15.5.3 FEEDFORWARD CONTROL WITH MULTIPLE INPUTS, 635 15.5.4
FEEDFORWARD-FEEDBACK CONTROL, 636 15.5.5 ADVANTAGES AND DISADVANTAGES OF
FEEDFORWARD AND FEEDBACK CONTROL, 638 -*" "^ 15.5.6 REMARKS ON FITTING
TRANSFER FUNCTION-NOISE MODELS USING OPERATING DATA, 639 15.6 MONITORING
VALUES OF PARAMETERS OF FORECASTING AND FEEDBACK ADJUSTMENT SCHEMES, 642
A 15.1 FEEDBACK CONTROL SCHEMES WHERE THE ADJUSTMENT VARIANCE IS
RESTRICTED, 644 [ A15.1.1 DERIVATION OF OPTIMAL ADJUSTMENT, 644 A15.2
CHOICE OF THE SAMPLING INTERVAL, 653 A15.2.1 ILLUSTRATION OF THE EFFECT
OF REDUCING SAMPLING FREQUENCY, 654 A 15.2.2 SAMPLING AN IMA(0, 1,1)
PROCESS, 654 XX CONTENTS PART FIVE CHARTS AND TABLES 659 COLLECTION OF
TABLES AND CHARTS 661 COLLECTION OF TIME SERIES USED FOR EXAMPLES IN THE
TEXT AND IN EXERCISES 669 REFERENCES 685 PART SIX EXERCISES AND PROBLEMS
701 INDEX 729 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Box, George E. P. 1919-2013 Jenkins, Gwilym M. 1932-1982 Reinsel, Gregory C. 1948-2004 |
| author_GND | (DE-588)108415066 (DE-588)131749374 (DE-588)113599382 |
| author_facet | Box, George E. P. 1919-2013 Jenkins, Gwilym M. 1932-1982 Reinsel, Gregory C. 1948-2004 |
| author_role | 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 |
| building | Verbundindex |
| bvnumber | BV023024269 |
| callnumber-first | Q - Science |
| callnumber-label | QA280 |
| callnumber-raw | QA280 |
| callnumber-search | QA280 |
| callnumber-sort | QA 3280 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 845 |
| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)882079441 (DE-599)HBZHT015651788 |
| 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 |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV023024269 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:14:27Z |
| indexdate | 2024-07-09T21:09:14Z |
| institution | BVB |
| isbn | 9780470272848 9781118619193 |
| language | English |
| lccn | 2007044569 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016228271 |
| oclc_num | 882079441 |
| open_access_boolean | |
| owner | DE-703 DE-573 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-11 DE-945 DE-384 DE-29 |
| owner_facet | DE-703 DE-573 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-11 DE-945 DE-384 DE-29 |
| physical | XXIV, 746 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Box, George E. P. 1919-2013 Verfasser (DE-588)108415066 aut Time series analysis forecasting and control George E. P. Box ; Gwilym M. Jenkins ; Gregory C. Reinsel 4. ed. Hoboken, NJ Wiley 2008 XXIV, 746 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Literaturverz. S. 685 - 699 Análise de séries temporais larpcal Mathematisches Modell Feedback control systems Mathematical models Prediction theory Time-series analysis Transfer functions Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf 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 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 Verfasser (DE-588)131749374 aut Reinsel, Gregory C. 1948-2004 Verfasser (DE-588)113599382 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016228271&sequence=000001&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 Time series analysis forecasting and control Análise de séries temporais larpcal Mathematisches Modell Feedback control systems Mathematical models Prediction theory Time-series analysis Transfer functions Stochastisches Modell (DE-588)4057633-4 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastik (DE-588)4121729-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4013396-5 (DE-588)4121729-9 (DE-588)4067486-1 |
| 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_exact_search_txtP | Time series analysis forecasting and control |
| title_full | Time series analysis forecasting and control George E. P. Box ; Gwilym M. Jenkins ; Gregory C. Reinsel |
| title_fullStr | Time series analysis forecasting and control George E. P. Box ; Gwilym M. Jenkins ; Gregory C. Reinsel |
| title_full_unstemmed | Time series analysis forecasting and control George E. P. Box ; Gwilym M. Jenkins ; Gregory C. Reinsel |
| title_short | Time series analysis |
| title_sort | time series analysis forecasting and control |
| title_sub | forecasting and control |
| topic | Análise de séries temporais larpcal Mathematisches Modell Feedback control systems Mathematical models Prediction theory Time-series analysis Transfer functions Stochastisches Modell (DE-588)4057633-4 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastik (DE-588)4121729-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Análise de séries temporais Mathematisches Modell Feedback control systems Mathematical models Prediction theory Time-series analysis Transfer functions Stochastisches Modell Dynamisches System Stochastik Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016228271&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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