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Bibliographic Details
Main Authors:	Box, George E. P. 1919-2013 (Author), Jenkins, Gwilym M. 1932-1982 (Author), Reinsel, Gregory C. 1948-2004 (Author)
Format:	Book
Language:	English
Published:	Hoboken, NJ Wiley 2008
Edition:	4. ed.
Series:	Wiley series in probability and statistics
Subjects:	Análise de séries temporais Mathematisches Modell Feedback control systems > Mathematical models Prediction theory Time-series analysis Transfer functions Stochastisches Modell Dynamisches System Stochastik Zeitreihenanalyse
Links:	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
Item Description:	Literaturverz. S. 685 - 699
Physical Description:	XXIV, 746 S. Ill., graph. Darst.
ISBN:	9780470272848 9781118619193

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Record in the Search Index

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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 EXAMPLECONTROL 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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author	Box, George E. P. 1919-2013 Jenkins, Gwilym M. 1932-1982 Reinsel, Gregory C. 1948-2004
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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
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indexdate	2024-12-20T13:06:51Z
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isbn	9780470272848 9781118619193
language	English
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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.
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series2	Wiley series in probability and statistics
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_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
work_keys_str_mv	AT boxgeorgeep timeseriesanalysisforecastingandcontrol AT jenkinsgwilymm timeseriesanalysisforecastingandcontrol AT reinselgregoryc timeseriesanalysisforecastingandcontrol

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