New introduction to multiple time series analysis: with 36 tables
Gespeichert in:
| Vorheriger Titel: | Lütkepohl, Helmut Introduction to multiple time series analysis |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 713 - 732 |
| Beschreibung: | XXI, 764 S. graph. Darst. |
| ISBN: | 3540401725 3540262393 9783540401728 9783540262398 |
Internformat
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| 100 | 1 | |a Lütkepohl, Helmut |d 1951- |e Verfasser |0 (DE-588)10979544X |4 aut | |
| 245 | 1 | 0 | |a New introduction to multiple time series analysis |b with 36 tables |c Helmut Lütkepohl |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a XXI, 764 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 713 - 732 | ||
| 650 | 4 | |a Time-series analysis | |
| 650 | 0 | 7 | |a Multiple Zeitreihenanalyse |0 (DE-588)4290989-2 |2 gnd |9 rswk-swf |
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| 780 | 0 | 0 | |i 931112184 Früher u.d.T. |a Lütkepohl, Helmut |t Introduction to multiple time series analysis |
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Datensatz im Suchindex
| _version_ | 1804133423158132736 |
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| adam_text | LÜTKEPOHL
New
This reference work and graduate level textbook considers a wide
range of models and methods for analyzing and forecasting multiple
time series. The models covered include vector
«integrated, vector
ARCH and periodic processes as well as dynamic simultaneous
equations and state space models. Least squares» maximum likelihood,
and Bayesian methods are considered for estimating
Different procedures for model selection and model specification
are treated and a wide range of tests and criteria for model checking
are introduced. Causality analysis, impulse response analysis and
innovation accounting are presented as tools for structural analy-
sis.The book is accessible to graduate students in business and
economics. In addition, multiple time series courses in other fields
such as statistics and engineering may be based on it. Applied
researchers involved in analyzing multiple time series may benefit
from the book as it provides the background and tools for their tasks.
It bridges the gap to the difficult technical literature on the topic.
HELMUT LIITKEPOHL NEW INTRODUCTION TO MULTIPLE TIME SERIES ANALYSIS WITH
49 FIGURES AND 36 TABLES ^J SPRINGER CONTENTS 1 INTRODUCTION 1 1.1
OBJECTIVES OF ANALYZING MULTIPLE TIME SERIES 1 1.2 SOME BASICS 2 1.3
VECTOR AUTOREGRESSIVE PROCESSES 4 1.4 OUTLINE OF THE FOLLOWING CHAPTERS
5 PART I FINITE ORDER VECTOR AUTOREGRESSIVE PROCESSES 2 STABLE VECTOR
AUTOREGRESSIVE PROCESSES 13 2.1 BASIC ASSUMPTIONS AND PROPERTIES OF VAR
PROCESSES 13 2.1.1 STABLE VAR(P) PROCESSES 13 2.1.2 THE MOVING AVERAGE
REPRESENTATION OF A VAR PROCESS . 18 2.1.3 STATIONARY PROCESSES 24 2.1.4
COMPUTATION OF AUTOCOVARIANCES AND AUTOCORRELATIONS OF STABLE VAR
PROCESSES 26 2.2 FORECASTING 31 2.2.1 THE LOSS FUNCTION 32 2.2.2 POINT
FORECASTS 33 2.2.3 INTERVAL FORECASTS AND FORECAST REGIONS 39 2.3
STRUCTURAL ANALYSIS WITH VAR MODELS 41 2.3.1 GRANGER-CAUSALITY,
INSTANTANEOUS CAUSALITY, AND MULTI-STEP CAUSALITY 41 2.3.2 IMPULSE
RESPONSE ANALYSIS 51 2.3.3 FORECAST ERROR VARIANCE DECOMPOSITION 63
2.3.4 REMARKS ON THE INTERPRETATION OF VAR MODELS 66 2.4 EXERCISES 66 3
ESTIMATION OF VECTOR AUTOREGRESSIVE PROCESSES 69 3.1 INTRODUCTION 69 3.2
MULTIVARIATE LEAST SQUARES ESTIMATION 69 XII CONTENTS 3.2.1 THE
ESTIMATOR 70 3.2.2 ASYMPTOTIC PROPERTIES OF THE LEAST SQUARES ESTIMATOR
. 73 3.2.3 AN EXAMPLE 77 3.2.4 SMALL SAMPLE PROPERTIES OF THE LS
ESTIMATOR 80 3.3 LEAST SQUARES ESTIMATION WITH MEAN-ADJUSTED DATA AND
YULE-WALKER ESTIMATION 82 3.3.1 ESTIMATION WHEN THE PROCESS MEAN IS
KNOWN 82 3.3.2 ESTIMATION OF THE PROCESS MEAN 83 3.3.3 ESTIMATION WITH
UNKNOWN PROCESS MEAN 85 3.3.4 THE YULE-WALKER ESTIMATOR 85 3.3.5 AN
EXAMPLE 87 3.4 MAXIMUM LIKELIHOOD ESTIMATION 87 3.4.1 THE LIKELIHOOD
FUNCTION 87 3.4.2 THE ML ESTIMATORS 89 3.4.3 PROPERTIES OF THE ML
ESTIMATORS 90 3.5 FORECASTING WITH ESTIMATED PROCESSES 94 3.5.1 GENERAL
ASSUMPTIONS AND RESULTS 94 3.5.2 THE APPROXIMATE MSE MATRIX 96 3.5.3 AN
EXAMPLE 98 3.5.4 A SMALL SAMPLE INVESTIGATION 100 3.6 TESTING FOR
CAUSALITY 102 3.6.1 A WALD TEST FOR GRANGER-CAUSALITY 102 3.6.2 AN
EXAMPLE 103 3.6.3 TESTING FOR INSTANTANEOUS CAUSALITY 104 3.6.4 TESTING
FOR MULTI-STEP CAUSALITY 106 3.7 THE ASYMPTOTIC DISTRIBUTIONS OF IMPULSE
RESPONSES AND FORECAST ERROR VARIANCE DECOMPOSITIONS 109 3.7.1 THE MAIN
RESULTS 109 3.7.2 PROOF OF PROPOSITION 3.6 116 3.7.3 AN EXAMPLE 118
3.7.4 INVESTIGATING THE DISTRIBUTIONS OF THE IMPULSE RESPONSES BY
SIMULATION TECHNIQUES 126 3.8 EXERCISES 130 3.8.1 ALGEBRAIC PROBLEMS 130
3.8.2 NUMERICAL PROBLEMS 132 4 VAR ORDER SELECTION AND CHECKING THE
MODEL ADEQUACY . . 135 4.1 INTRODUCTION 135 4.2 A SEQUENCE OF TESTS FOR
DETERMINING THE VAR ORDER 136 4.2.1 THE IMPACT OF THE FITTED VAR ORDER
ON THE FORECAST MSE 136 4.2.2 THE LIKELIHOOD RATIO TEST STATISTIC 138
4.2.3 A TESTING SCHEME FOR VAR ORDER DETERMINATION 143 4.2.4 AN EXAMPLE
145 4.3 CRITERIA FOR VAR ORDER SELECTION 146 CONTENTS XIII 4.3.1
MINIMIZING THE FORECAST MSE 146 4.3.2 CONSISTENT ORDER SELECTION 148
4.3.3 COMPARISON OF ORDER SELECTION CRITERIA 151 4.3.4 SOME SMALL SAMPLE
SIMULATION RESULTS 153 4.4 CHECKING THE WHITENESS OF THE RESIDUALS 157
4.4.1 THE ASYMPTOTIC DISTRIBUTIONS OF THE AUTOCOVARIANCES AND
AUTOCORRELATIONS OF A WHITE NOISE PROCESS 157 4.4.2 THE ASYMPTOTIC
DISTRIBUTIONS OF THE RESIDUAL AUTOCOVARIANCES AND AUTOCORRELATIONS OF AN
ESTIMATED VAR PROCESS 161 4.4.3 PORTMANTEAU TESTS 169 4.4.4 LAGRANGE
MULTIPLIER TESTS 171 4.5 TESTING FOR NONNORMALITY 174 4.5.1 TESTS FOR
NONNORMALITY OF A VECTOR WHITE NOISE PROCESS 174 4.5.2 TESTS FOR
NONNORMALITY OF A VAR PROCESS 177 4.6 TESTS FOR STRUCTURAL CHANGE 181
4.6.1 CHOW TESTS 182 4.6.2 FORECAST TESTS FOR STRUCTURAL CHANGE 184 4.7
EXERCISES 189 4.7.1 ALGEBRAIC PROBLEMS 189 4.7.2 NUMERICAL PROBLEMS 191
VAR PROCESSES WITH PARAMETER CONSTRAINTS 193 5.1 INTRODUCTION 193 5.2
LINEAR CONSTRAINTS 194 5.2.1 THE MODEL AND THE CONSTRAINTS 194 5.2.2 LS,
GLS, AND EGLS ESTIMATION 195 5.2.3 MAXIMUM LIKELIHOOD ESTIMATION 200
5.2.4 CONSTRAINTS FOR INDIVIDUAL EQUATIONS 201 5.2.5 RESTRICTIONS FOR
THE WHITE NOISE COVARIANCE MATRIX.... 202 5.2.6 FORECASTING 204 5.2.7
IMPULSE RESPONSE ANALYSIS AND FORECAST ERROR VARIANCE DECOMPOSITION 205
5.2.8 SPECIFICATION OF SUBSET VAR MODELS 206 5.2.9 MODEL CHECKING 212
5.2.10 AN EXAMPLE 217 5.3 VAR PROCESSES WITH NONLINEAR PARAMETER
RESTRICTIONS 221 5.4 BAYESIAN ESTIMATION 222 5.4.1 BASIC TERMS AND
NOTATION 222 5.4.2 NORMAL PRIORS FOR THE PARAMETERS OF A GAUSSIAN VAR
PROCESS 223 5.4.3 THE MINNESOTA OR LITTERMAN PRIOR 225 5.4.4 PRACTICAL
CONSIDERATIONS 227 5.4.5 AN EXAMPLE 227 XIV CONTENTS 5.4.6 CLASSICAL
VERSUS BAYESIAN INTERPRETATION OF A IN FORECASTING AND STRUCTURAL
ANALYSIS 228 5.5 EXERCISES 230 5.5.1 ALGEBRAIC EXERCISES 230 5.5.2
NUMERICAL PROBLEMS 231 PART II COINTEGRATED PROCESSES 6 VECTOR ERROR
CORRECTION MODELS 237 6.1 INTEGRATED PROCESSES 238 6.2 VAR PROCESSES
WITH INTEGRATED VARIABLES 243 6.3 COINTEGRATED PROCESSES, COMMON
STOCHASTIC TRENDS, AND VECTOR ERROR CORRECTION MODELS 244 6.4
DETERMINISTIC TERMS IN COINTEGRATED PROCESSES 256 6.5 FORECASTING
INTEGRATED AND COINTEGRATED VARIABLES 258 6.6 CAUSALITY ANALYSIS 261 6.7
IMPULSE RESPONSE ANALYSIS 262 6.8 EXERCISES 265 7 ESTIMATION OF VECTOR
ERROR CORRECTION MODELS 269 7.1 ESTIMATION OF A SIMPLE SPECIAL CASE VECM
269 7.2 ESTIMATION OF GENERAL VECMS 286 7.2.1 LS ESTIMATION 287 7.2.2
EGLS ESTIMATION OF THE COINTEGRATION PARAMETERS .... 291 7.2.3 ML
ESTIMATION 294 7.2.4 INCLUDING DETERMINISTIC TERMS 299 7.2.5 OTHER
ESTIMATION METHODS FOR COINTEGRATED SYSTEMS. . . 300 7.2.6 AN EXAMPLE
302 7.3 ESTIMATING VECMS WITH PARAMETER RESTRICTIONS 305 7.3.1 LINEAR
RESTRICTIONS FOR THE COINTEGRATION MATRIX 305 7.3.2 LINEAR RESTRICTIONS
FOR THE SHORT-RUN AND LOADING PARAMETERS 307 7.3.3 AN EXAMPLE 309 7.4
BAYESIAN ESTIMATION OF INTEGRATED SYSTEMS 309 7.4.1 THE MODEL SETUP 310
7.4.2 THE MINNESOTA OR LITTERMAN PRIOR 310 7.4.3 AN EXAMPLE 312 7.5
FORECASTING ESTIMATED INTEGRATED AND COINTEGRATED SYSTEMS . . 315 7.6
TESTING FOR GRANGER-CAUSALITY 316 7.6.1 THE NONCAUSALITY RESTRICTIONS
316 7.6.2 PROBLEMS RELATED TO STANDARD WALD TESTS 317 7.6.3 A WALD TEST
BASED ON A LAG AUGMENTED VAR 318 7.6.4 AN EXAMPLE 320 7.7 IMPULSE
RESPONSE ANALYSIS 321 CONTENTS XV 7.8 EXERCISES 323 7.8.1 ALGEBRAIC
EXERCISES 323 7.8.2 NUMERICAL EXERCISES 324 SPECIFICATION OF VECMS 325
8.1 LAG ORDER SELECTION 325 8.2 TESTING FOR THE RANK OF COINTEGRATION
327 8.2.1 A VECM WITHOUT DETERMINISTIC TERMS 328 8.2.2 A NONZERO MEAN
TERM 330 8.2.3 A LINEAR TREND 331 8.2.4 A LINEAR TREND IN THE VARIABLES
AND NOT IN THE COINTEGRATION RELATIONS 331 8.2.5 SUMMARY OF RESULTS AND
OTHER DETERMINISTIC TERMS . . . 332 8.2.6 AN EXAMPLE 335 8.2.7 PRIOR
ADJUSTMENT FOR DETERMINISTIC TERMS 337 8.2.8 CHOICE OF DETERMINISTIC
TERMS 341 8.2.9 OTHER APPROACHES TO TESTING FOR THE COINTEGRATING
RANK342 8.3 SUBSET VECMS 343 8.4 MODEL DIAGNOSTICS 345 8.4.1 CHECKING
FOR RESIDUAL AUTOCORRELATION 345 8.4.2 TESTING FOR NONNORMALITY 348
8.4.3 TESTS FOR STRUCTURAL CHANGE 348 8.5 EXERCISES 351 8.5.1 ALGEBRAIC
EXERCISES 351 8.5.2 NUMERICAL EXERCISES 352 PART III STRUCTURAL AND
CONDITIONAL MODELS 9 STRUCTURAL VARS AND VECMS 357 9.1 STRUCTURAL VECTOR
AUTOREGRESSIONS 358 9.1.1 THE A-MODEL 358 9.1.2 THE B-MODEL 362 9.1.3
THE AB-MODEL 364 9.1.4 LONG-RUN RESTRICTIONS A LA BLANCHARD-QUAH 367 9.2
STRUCTURAL VECTOR ERROR CORRECTION MODELS 368 9.3 ESTIMATION OF
STRUCTURAL PARAMETERS 372 9.3.1 ESTIMATING SVAR MODELS 372 9.3.2
ESTIMATING STRUCTURAL VECMS 376 9.4 IMPULSE RESPONSE ANALYSIS AND
FORECAST ERROR VARIANCE DECOMPOSITION 377 9.5 FURTHER ISSUES 383 9.6
EXERCISES 384 9.6.1 ALGEBRAIC PROBLEMS 384 9.6.2 NUMERICAL PROBLEMS 385
XVI CONTENTS 10 SYSTEMS OF DYNAMIC SIMULTANEOUS EQUATIONS 387 10.1
BACKGROUND 387 10.2 SYSTEMS WITH UNMODELLED VARIABLES 388 10.2.1 TYPES
OF VARIABLES 388 10.2.2 STRUCTURAL FORM, REDUCED FORM, FINAL FORM 390
10.2.3 MODELS WITH RATIONAL EXPECTATIONS 393 10.2.4 COINTEGRATED
VARIABLES 394 10.3 ESTIMATION 395 10.3.1 STATIONARY VARIABLES 396 10.3.2
ESTIMATION OF MODELS WITH 7(1) VARIABLES 398 10.4 REMARKS ON MODEL
SPECIFICATION AND MODEL CHECKING 400 10.5 FORECASTING 401 10.5.1
UNCONDITIONAL AND CONDITIONAL FORECASTS 401 10.5.2 FORECASTING ESTIMATED
DYNAMIC SEMS 405 10.6 MULTIPLIER ANALYSIS 406 10.7 OPTIMAL CONTROL 408
10.8 CONCLUDING REMARKS ON DYNAMIC SEMS 411 10.9 EXERCISES 412 PART IV
INFINITE ORDER VECTOR AUTOREGRESSIVE PROCESSES 11 VECTOR AUTOREGRESSIVE
MOVING AVERAGE PROCESSES 419 11.1 INTRODUCTION 419 11.2 FINITE ORDER
MOVING AVERAGE PROCESSES 420 11.3 VARMA PROCESSES 423 11.3.1 THE PURE MA
AND PURE VAR REPRESENTATIONS OF A VARMA PROCESS 423 11.3.2 A VAR(L)
REPRESENTATION OF A VARMA PROCESS 426 11.4 THE AUTOCOVARIANCES AND
AUTOCORRELATIONS OF A VARMA(P, Q) PROCESS 429 11.5 FORECASTING VARMA
PROCESSES 432 11.6 TRANSFORMING AND AGGREGATING VARMA PROCESSES 434
11.6.1 LINEAR TRANSFORMATIONS OF VARMA PROCESSES 435 11.6.2 AGGREGATION
OF VARMA PROCESSES 440 11.7 INTERPRETATION OF VARMA MODELS 442 11.7.1
GRANGER-CAUSALITY 442 11.7.2 IMPULSE RESPONSE ANALYSIS 444 11.8
EXERCISES 444 12 ESTIMATION OF VARMA MODELS 447 12.1 THE IDENTIFICATION
PROBLEM 447 12.1.1 NONUNIQUENESS OF VARMA REPRESENTATIONS 447 12.1.2
FINAL EQUATIONS FORM AND ECHELON FORM 452 12.1.3 ILLUSTRATIONS 455
CONTENTS XVII 12.2 THE GAUSSIAN LIKELIHOOD FUNCTION 459 12.2.1 THE
LIKELIHOOD FUNCTION OF AN MA(1) PROCESS 459 12.2.2 THE MA(Q) CASE 461
12.2.3 THE VARMA(1,1) CASE 463 12.2.4 THE GENERAL VARMA(P, Q) CASE 464
12.3 COMPUTATION OF THE ML ESTIMATES 467 12.3.1 THE NORMAL EQUATIONS 468
12.3.2 OPTIMIZATION ALGORITHMS 470 12.3.3 THE INFORMATION MATRIX 473
12.3.4 PRELIMINARY ESTIMATION 474 12.3.5 AN ILLUSTRATION 477 12.4
ASYMPTOTIC PROPERTIES OF THE ML ESTIMATORS 479 12.4.1 THEORETICAL
RESULTS 479 12.4.2 A REAL DATA EXAMPLE 486 12.5 FORECASTING ESTIMATED
VARMA PROCESSES 487 12.6 ESTIMATED IMPULSE RESPONSES 490 12.7 EXERCISES
491 13 SPECIFICATION AND CHECKING THE ADEQUACY OF VARMA MODELS 493 13.1
INTRODUCTION 493 13.2 SPECIFICATION OF THE FINAL EQUATIONS FORM 494
13.2.1 A SPECIFICATION PROCEDURE 494 13.2.2 AN EXAMPLE 497 13.3
SPECIFICATION OF ECHELON FORMS 498 13.3.1 A PROCEDURE FOR SMALL SYSTEMS
499 13.3.2 A FULL SEARCH PROCEDURE BASED ON LINEAR LEAST SQUARES
COMPUTATIONS 501 13.3.3 HANNAN-KAVALIERIS PROCEDURE 503 13.3.4 POSKITT S
PROCEDURE 505 13.4 REMARKS ON OTHER SPECIFICATION STRATEGIES FOR VARMA
MODELS 507 13.5 MODEL CHECKING 508 13.5.1 LM TESTS 508 13.5.2 RESIDUAL
AUTOCORRELATIONS AND PORTMANTEAU TESTS 510 13.5.3 PREDICTION TESTS FOR
STRUCTURAL CHANGE 511 13.6 CRITIQUE OF VARMA MODEL FITTING 511 13.7
EXERCISES 512 14 COINTEGRATED VARMA PROCESSES 515 14.1 INTRODUCTION 515
14.2 THE VARMA FRAMEWORK FOR 7(1) VARIABLES 516 14.2.1 LEVELS VARMA
MODELS 516 14.2.2 THE REVERSE ECHELON FORM 518 14.2.3 THE ERROR
CORRECTION ECHELON FORM 519 14.3 ESTIMATION 521 XVIII CONTENTS 14.3.1
ESTIMATION OF ARMA FLB MODELS 521 14.3.2 ESTIMATION OF EC-ARMA FLB
MODELS 522 14.4 SPECIFICATION OF EC-ARMA^ MODELS 523 14.4.1
SPECIFICATION OF KRONECKER INDICES 523 14.4.2 SPECIFICATION OF THE
COINTEGRATING RANK 525 14.5 FORECASTING COINTEGRATED VARMA PROCESSES 526
14.6 AN EXAMPLE 526 14.7 EXERCISES 528 14.7.1 ALGEBRAIC EXERCISES 528
14.7.2 NUMERICAL EXERCISES 529 15 FITTING FINITE ORDER VAR MODELS TO
INFINITE ORDER PROCESSES 531 15.1 BACKGROUND 531 15.2 MULTIVARIATE LEAST
SQUARES ESTIMATION 532 15.3 FORECASTING 536 15.3.1 THEORETICAL RESULTS
536 15.3.2 AN EXAMPLE 538 15.4 IMPULSE RESPONSE ANALYSIS AND FORECAST
ERROR VARIANCE DECOMPOSITIONS 540 15.4.1 ASYMPTOTIC THEORY 540 15.4.2 AN
EXAMPLE 543 15.5 COINTEGRATED INFINITE ORDER VARS 545 15.5.1 THE MODEL
SETUP 546 15.5.2 ESTIMATION 549 15.5.3 TESTING FOR THE COINTEGRATING
RANK 551 15.6 EXERCISES 552 PART V TIME SERIES TOPICS 16 MULTIVARIATE
ARCH AND GARCH MODELS 557 16.1 BACKGROUND 557 16.2 UNIVARIATE GARCH
MODELS 559 16.2.1 DEFINITIONS 559 16.2.2 FORECASTING 561 16.3
MULTIVARIATE GARCH MODELS 562 16.3.1 MULTIVARIATE ARCH 563 16.3.2 MGARCH
564 16.3.3 OTHER MULTIVARIATE ARCH AND GARCH MODELS 567 16.4 ESTIMATION
569 16.4.1 THEORY 569 16.4.2 AN EXAMPLE 571 16.5 CHECKING MGARCH MODELS
576 16.5.1 ARCH-LM AND ARCH-PORTMANTEAU TESTS 576 CONTENTS XIX 16.5.2 LM
AND PORTMANTEAU TESTS FOR REMAINING ARCH 577 16.5.3 OTHER DIAGNOSTIC
TESTS 578 16.5.4 AN EXAMPLE 578 16.6 INTERPRETING GARCH MODELS 579
16.6.1 CAUSALITY IN VARIANCE 579 16.6.2 CONDITIONAL MOMENT PROFILES AND
GENERALIZED IMPULSE RESPONSES 580 16.7 PROBLEMS AND EXTENSIONS 582 16.8
EXERCISES 584 17 PERIODIC VAR PROCESSES AND INTERVENTION MODELS 585 17.1
INTRODUCTION 585 17.2 THE VAR(P) MODEL WITH TIME VARYING COEFFICIENTS
587 17.2.1 GENERAL PROPERTIES 587 17.2.2 ML ESTIMATION 589 17.3 PERIODIC
PROCESSES 591 17.3.1 A VAR REPRESENTATION WITH TIME INVARIANT
COEFFICIENTS 592 17.3.2 ML ESTIMATION AND TESTING FOR TIME VARYING
COEFFICIENTS 595 17.3.3 AN EXAMPLE 602 17.3.4 BIBLIOGRAPHICAL NOTES AND
EXTENSIONS 604 17.4 INTERVENTION MODELS 604 17A.I INTERVENTIONS IN THE
INTERCEPT MODEL 605 17.4.2 A DISCRETE CHANGE IN THE MEAN 606 17.4.3 AN
ILLUSTRATIVE EXAMPLE 608 17.4.4 EXTENSIONS AND REFERENCES 609 17.5
EXERCISES 609 18 STATE SPACE MODELS 611 18.1 BACKGROUND 611 18.2 STATE
SPACE MODELS 613 18.2.1 THE MODEL SETUP 613 18.2.2 MORE GENERAL STATE
SPACE MODELS 624 18.3 THE KALMAN FILTER 625 18.3.1 THE KALMAN FILTER
RECURSIONS 626 18.3.2 PROOF OF THE KALMAN FILTER RECURSIONS 630 18.4
MAXIMUM LIKELIHOOD ESTIMATION OF STATE SPACE MODELS 631 18.4.1 THE
LOG-LIKELIHOOD FUNCTION 632 18.4.2 THE IDENTIFICATION PROBLEM 633 18.4.3
MAXIMIZATION OF THE LOG-LIKELIHOOD FUNCTION 634 18.4.4 ASYMPTOTIC
PROPERTIES OF THE ML ESTIMATOR 636 18.5 A REAL DATA EXAMPLE 637 18.6
EXERCISES 641 XX CONTENTS APPENDIX A VECTORS AND MATRICES 645 A.I BASIC
DEFINITIONS 645 A.2 BASIC MATRIX OPERATIONS 646 A.3 THE DETERMINANT 647
A.4 THE INVERSE, THE ADJOINT, AND GENERALIZED INVERSES 649 A.4.1 INVERSE
AND ADJOINT OF A SQUARE MATRIX 649 A.4.2 GENERALIZED INVERSES 650 A.5
THE RANK 651 A.6 EIGENVALUES AND -VECTORS - CHARACTERISTIC VALUES AND
VECTORS. . 652 A.7 THE TRACE 653 A.8 SOME SPECIAL MATRICES AND VECTORS
653 A.8.1 IDEMPOTENT AND NILPOTENT MATRICES 653 A.8.2 ORTHOGONAL
MATRICES AND VECTORS AND ORTHOGONAL COMPLEMENTS 654 A.8.3 DEFINITE
MATRICES AND QUADRATIC FORMS 655 A.9 DECOMPOSITION AND DIAGONALIZATION
OF MATRICES 656 A.9.1 THE JORDAN CANONICAL FORM 656 A.9.2 DECOMPOSITION
OF SYMMETRIC MATRICES 658 A.9.3 THE CHOLESKI DECOMPOSITION OF A POSITIVE
DEFINITE MATRIX 658 A.10 PARTITIONED MATRICES 659 A.LL THE KRONECKER
PRODUCT 660 A. 12 THE VEC AND VECH OPERATORS AND RELATED MATRICES 661
A.12.1 THE OPERATORS 661 A.12.2 ELIMINATION, DUPLICATION, AND
COMMUTATION MATRICES . . 662 A. 13 VECTOR AND MATRIX DIFFERENTIATION 664
A.14 OPTIMIZATION OF VECTOR FUNCTIONS 671 A.15 PROBLEMS 675 B
MULTIVARIATE NORMAL AND RELATED DISTRIBUTIONS 677 B.I MULTIVARIATE
NORMAL DISTRIBUTIONS 677 B.2 RELATED DISTRIBUTIONS 678 C STOCHASTIC
CONVERGENCE AND ASYMPTOTIC DISTRIBUTIONS 68 1 C.I CONCEPTS OF STOCHASTIC
CONVERGENCE 681 C.2 ORDER IN PROBABILITY 684 C.3 INFINITE SUMS OF RANDOM
VARIABLES 685 C.4 LAWS OF LARGE NUMBERS AND CENTRAL LIMIT THEOREMS 689
C.5 STANDARD ASYMPTOTIC PROPERTIES OF ESTIMATORS AND TEST STATISTICS 692
C.6 MAXIMUM LIKELIHOOD ESTIMATION 693 C.7 LIKELIHOOD RATIO, LAGRANGE
MULTIPLIER, AND WALD TESTS 694 CONTENTS XXI C.8 UNIT ROOT ASYMPTOTICS
698 C.8.1 UNIVARIATE PROCESSES 698 C.8.2 MULTIVARIATE PROCESSES 703 D
EVALUATING PROPERTIES OF ESTIMATORS AND TEST STATISTICS BY SIMULATION
AND RESAMPLING TECHNIQUES 707 D.I SIMULATING A MULTIPLE TIME SERIES WITH
VAR GENERATION PROCESS 707 D.2 EVALUATING DISTRIBUTIONS OF FUNCTIONS OF
MULTIPLE TIME SERIES BY SIMULATION 708 D.3 RESAMPLING METHODS 709
REFERENCES 713 INDEX OF NOTATION 733 AUTHOR INDEX 741 SUBJECT INDEX 747
|
| any_adam_object | 1 |
| author | Lütkepohl, Helmut 1951- |
| author_GND | (DE-588)10979544X |
| author_facet | Lütkepohl, Helmut 1951- |
| author_role | aut |
| author_sort | Lütkepohl, Helmut 1951- |
| author_variant | h l hl |
| building | Verbundindex |
| bvnumber | BV019889175 |
| callnumber-first | Q - Science |
| callnumber-label | QA280 |
| callnumber-raw | QA280.L874 2005 |
| callnumber-search | QA280.L874 2005 |
| callnumber-sort | QA 3280 L874 42005 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | MR 2000 QH 237 SK 845 |
| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)314329755 (DE-599)BVBBV019889175 |
| dewey-full | 519.5/522 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 22 |
| dewey-search | 519.5/5 22 |
| dewey-sort | 3519.5 15 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV019889175 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:08:28Z |
| institution | BVB |
| isbn | 3540401725 3540262393 9783540401728 9783540262398 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013213217 |
| oclc_num | 314329755 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-945 DE-91G DE-BY-TUM DE-1047 DE-824 DE-29T DE-N2 DE-20 DE-384 DE-19 DE-BY-UBM DE-706 DE-521 DE-11 |
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| physical | XXI, 764 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| spelling | Lütkepohl, Helmut 1951- Verfasser (DE-588)10979544X aut New introduction to multiple time series analysis with 36 tables Helmut Lütkepohl Berlin [u.a.] Springer 2005 XXI, 764 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 713 - 732 Time-series analysis Multiple Zeitreihenanalyse (DE-588)4290989-2 gnd rswk-swf Multiple Zeitreihenanalyse (DE-588)4290989-2 s DE-604 931112184 Früher u.d.T. Lütkepohl, Helmut Introduction to multiple time series analysis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013213217&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013213217&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lütkepohl, Helmut 1951- New introduction to multiple time series analysis with 36 tables Time-series analysis Multiple Zeitreihenanalyse (DE-588)4290989-2 gnd |
| subject_GND | (DE-588)4290989-2 |
| title | New introduction to multiple time series analysis with 36 tables |
| title_auth | New introduction to multiple time series analysis with 36 tables |
| title_exact_search | New introduction to multiple time series analysis with 36 tables |
| title_full | New introduction to multiple time series analysis with 36 tables Helmut Lütkepohl |
| title_fullStr | New introduction to multiple time series analysis with 36 tables Helmut Lütkepohl |
| title_full_unstemmed | New introduction to multiple time series analysis with 36 tables Helmut Lütkepohl |
| title_old | Lütkepohl, Helmut Introduction to multiple time series analysis |
| title_short | New introduction to multiple time series analysis |
| title_sort | new introduction to multiple time series analysis with 36 tables |
| title_sub | with 36 tables |
| topic | Time-series analysis Multiple Zeitreihenanalyse (DE-588)4290989-2 gnd |
| topic_facet | Time-series analysis Multiple Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013213217&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013213217&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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