Elements of multivariate time series analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2003
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 332 - 344 |
| Beschreibung: | XVII, 357 S. graph. Darst. |
| ISBN: | 0387406190 9780387406190 |
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Datensatz im Suchindex
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| adam_text | GREGORY C. REINSEL ELEMENTS OF MULTIVARIATE TIME SERIES ANALYSIS SECOND
EDITION WITH 14 FIGURES SPRINGER CONTENTS PREFACE TO THE SECOND EDITION
VII PREFACE TO THE FIRST EDITION IX 1. VECTOR TIME SERIES AND MODEL
REPRESENTATIONS 1 1.1 STATIONARY MULTIVARIATE TIME SERIES AND THEIR
PROPERTIES 2 1.1.1 COVARIANCE AND CORRELATION MATRICES FOR A STATIONARY
VECTOR PROCESS 2 1.1.2 SOME SPECTRAL CHARACTERISTICS FOR A STATIONARY
VECTOR PROCESS 4 1.1.3 SOME RELATIONS FOR LINEAR FILTERING OF A
STATIONARY VECTOR PROCESS 5 1.2 LINEAR MODEL REPRESENTATIONS FOR A
STATIONARY VECTOR PROCESS .. 7 1.2.1 INFINITE MOVING AVERAGE (WOLD)
REPRESENTATION OF A STATIONARY VECTOR PROCESS 7 1.2.2 VECTOR
AUTOREGRESSIVE MOVING AVERAGE (ARMA) MODEL REPRESENTATIONS 7 AL
APPENDIX: REVIEW OF MULTIVARIATE NORMAL DISTRIBUTION AND RELATED TOPICS
12 AL.L REVIEW OF SOME BASIC MATRIX THEORY RESULTS 12 A1.2 VEC OPERATOR
AND KRONECKER PRODUCTS OF MATRICES 13 A1.3 EXPECTED VALUES AND
COVARIANCE MATRICES OF RANDOM VECTORS 14 A1.4 THE MULTIVARIATE NORMAL
DISTRIBUTION 14 A1.5 SOME BASIC RESULTS ON STOCHASTIC CONVERGENCE 19 2.
VECTOR ARMA TIME SERIES MODELS AND FORECASTING 22 2.1 VECTOR MOVING
AVERAGE MODELS 22 2.1.1 INVERTIBILITY OF THE VECTOR MOVING AVERAGE MODEL
22 XII . CONTENTS 2.1.2 COVARIANCE MATRICES OF THE VECTOR MOVING AVERAGE
MODEL 23 2.1.3 FEATURES OF THE VECTOR MA(1) MODEL 24 2.1.4 MODEL
STRUCTURE FOR SUBSET OF COMPONENTS IN THE VECTOR MA MODEL 25 2.2 VECTOR
AUTOREGRESSIVE MODELS 27 2.2.1 STATIONARITY OF THE VECTOR AUTOREGRESSIVE
MODEL 27 2.2.2 YULE-WALKER RELATIONS FOR COVARIANCE MATRICES OF A VECTOR
AR PROCESS 29 2.2.3 COVARIANCE FEATURES OF THE VECTOR AR(1) MODEL 29
2.2.4 UNIVARIATE MODEL STRUCTURE IMPLIED BY VECTOR AR MODEL ... 30 2.3
VECTOR MIXED AUTOREGRESSIVE MOVING AVERAGE MODELS 34 2.3.1 STATIONARITY
AND INVERTIBILITY OF THE VECTOR ARMA MODEL.... 34 2.3.2 RELATIONS FOR
THE COVARIANCE MATRICES OF THE VECTOR ARMA MODEL 35 2.3.3 SOME FEATURES
OF THE VECTOR ARMA(L.L) MODEL 36 2.3.4 CONSIDERATION OF PARAMETER
IDENTIFIABILITY FOR VECTOR ARMA MODELS 37 2.3.5 FURTHER ASPECTS OF
NONUNIQUENESS OF VECTOR ARMA MODEL REPRESENTATIONS 40 2.4 NONSTATIONARY
VECTOR ARMA MODELS 41 2.4.1 VECTOR ARIMA MODELS FOR NONSTATIONARY
PROCESSES 42 2.4.2 COINTEGRATION IN NONSTATIONARY VECTOR PROCESSES 43
2.4.3 THE VECTOR IMA(L.L) PROCESS OR EXPONENTIAL SMOOTHING MODEL 44 2.5
PREDICTION FOR VECTOR ARMA MODELS 46 2.5.1 MINIMUM MEAN SQUARED ERROR
PREDICTION 47 2.5.2 FORECASTING FOR VECTOR ARMA PROCESSES AND COVARIANCE
MATRICES OF FORECAST ERRORS 47 2.5.3 COMPUTATION OF FORECASTS FOR VECTOR
ARMA PROCESSES 49 2.5.4 SOME EXAMPLES OF FORECAST FUNCTIONS FOR VECTOR
ARMA MODELS 50 2.6 STATE-SPACE FORM OF THE VECTOR ARMA MODEL 52 A2
APPENDIX: METHODS FOR OBTAINING AUTOREGRESSIVE AND / MOVING AVERAGE
PARAMETERS FROM COVARIANCE MATRICES 56 A2.1 ITERATIVE ALGORITHM FOR
FACTORIZATION OF MOVING AVERAGE SPECTRAL DENSITY MATRIX IN TERMS OF
COVARIANCE MATRICES 56 A2.2 AUTOREGRESSIVE AND MOVING AVERAGE PARAMETER
MATRICES IN TERMS OF COVARIANCE MATRICES FOR THE VECTOR ARMA MODEL 58
A2.3 EVALUATION OF COVARIANCE MATRICES IN TERMS OF THE AR AND MA
PARAMETERS FOR THE VECTOR ARMA MODEL 59 CONTENTS 3. CANONICAL STRUCTURE
OF VECTOR ARMA MODELS 61 3.1 CONSIDERATION OF KRONECKER STRUCTURE FOR
VECTOR ARMA MODELS 61 3.1.1 KRONECKER INDICES AND MCMILLAN DEGREE OF
VECTOR ARMA PROCESS 62 3.1.2 ECHELON FORM STRUCTURE OF VECTOR ARMA MODEL
IMPLIED BY KRONECKER INDICES 63 3.1.3 REDUCED-RANK FORM OF VECTOR ARMA
MODEL IMPLIED BY KRONECKER INDICES 65 3.2 CANONICAL CORRELATION
STRUCTURE FOR ARMA TIME SERIES 68 3.2.1 REVIEW OF CANONICAL CORRELATIONS
IN MULTIVARIATE ANALYSIS 68 3.2.2 CANONICAL CORRELATIONS FOR VECTOR ARMA
PROCESSES 70 3.2.3 RELATION TO SCALAR COMPONENT MODEL STRUCTURE 71 3.3
PARTIAL AUTOREGRESSIVE AND PARTIAL CORRELATION MATRICES 74 3.3.1 VECTOR
AUTOREGRESSIVE MODEL APPROXIMATIONS AND PARTIAL AUTOREGRESSION MATRICES
74 3.3.2 RECURSIVE FITTING OF VECTOR AR MODEL APPROXIMATIONS 76 3.3.3
PARTIAL CROSS-CORRELATION MATRICES FOR A STATIONARY VECTOR PROCESS 79
3.3.4 PARTIAL CANONICAL CORRELATIONS FOR A STATIONARY VECTOR PROCESS 81
4. INITIAL MODEL BUILDING AND LEAST SQUARES ESTIMATION FOR VECTOR AR
MODELS 84 4.1 SAMPLE CROSS-COVARIANCE AND CORRELATION MATRICES AND THEIR
PROPERTIES 84 4.1.1 SAMPLE ESTIMATES OF MEAN VECTOR AND OF COVARIANCE
AND CORRELATION MATRICES 84 4.1.2 ASYMPTOTIC PROPERTIES OF SAMPLE
CORRELATIONS 86 4.2 SAMPLE PARTIAL AR AND PARTIAL CORRELATION MATRICES
AND THEIR PROPERTIES 88 4.2.1 TEST FOR ORDER OF AR MODEL BASED ON SAMPLE
PARTIAL AUTOREGRESSION MATRICES 89 4.2.2 EQUIVALENT TEST STATISTICS
BASED ON SAMPLE PARTIAL CORRELATION MATRICES 89 4.3 CONDITIONAL LEAST
SQUARES ESTIMATION OF VECTOR AR MODELS 91 4.3.1 LEAST SQUARES ESTIMATION
FOR THE VECTOR AR(1) MODEL 91 4.3.2 LEAST SQUARES ESTIMATION FOR THE
VECTOR AR MODEL OF GENERAL ORDER 93 4.3.3 LIKELIHOOD RATIO TESTING FOR
THE ORDER OF THE AR MODEL 95 XIV CONTENTS 4.3.4 DERIVATION OF THE WALD
STATISTIC FOR TESTING THE ORDER OF THE AR MODEL 95 4.4 RELATION OF LSE
TO YULE-WALKER ESTIMATE FOR VECTOR AR MODELS 99 4.5 ADDITIONAL
TECHNIQUES FOR SPECIFICATION OF VECTOR ARMA MODELS 101 4.5.1 USE OF
ORDER SELECTION CRITERIA FOR MODEL SPECIFICATION 102 4.5.2 SAMPLE
CANONICAL CORRELATION ANALYSIS METHODS 103 4.5.3 ORDER DETERMINATION
USING LINEAR LSE METHODS FOR THE VECTOR ARMA MODEL 106 A4 APPENDIX:
REVIEW OF THE GENERAL MULTIVARIATE LINEAR REGRESSION MODEL 115 A4.1
PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE REGRESSION MATRIX
115 A4.2 LIKELIHOOD RATIO TEST OF LINEAR HYPOTHESIS ABOUT REGRESSION
COEFFICIENTS 116 A4.3 ASYMPTOTICALLY EQUIVALENT FORMS OF THE TEST OF
LINEAR HYPOTHESIS F. 118 A4.4 MULTIVARIATE LINEAR MODEL WITH
REDUCED-RANK STRUCTURE 119 A4.5 GENERALIZATION TO SEEMINGLY UNRELATED
REGRESSIONS MODEL 120 5. MAXIMUM LIKELIHOOD ESTIMATION AND MODEL
CHECKING FOR VECTOR ARMA MODELS 122 5.1 CONDITIONAL MAXIMUM LIKELIHOOD
ESTIMATION FOR VECTOR ARMA MODELS 122 5.1.1 CONDITIONAL LIKELIHOOD
FUNCTION FOR THE VECTOR ARMA MODEL 123 5.1.2 LIKELIHOOD EQUATIONS FOR
CONDITIONAL ML ESTIMATION 124 5.1.3 ITERATIVE COMPUTATION OF THE
CONDITIONAL MLE BY GLS ESTIMATION : 125 5.1.4 ASYMPTOTIC DISTRIBUTION
FOR THE MLE IN THE VECTOR ARMA MODEL 129 5.2 ML ESTIMATION AND LR
TESTING OF ARMA MODELS UNDER LINEAR RESTRICTIONS 130 5.2.1 ML ESTIMATION
OF VECTOR ARMA MODELS WITH LINEAR CONSTRAINTS ON THE PARAMETERS 130
5.2.2 LR TESTING OF THE HYPOTHESIS OF THE LINEAR CONSTRAINTS 132 5.2.3
ML ESTIMATION OF VECTOR ARMA MODELS IN THE ECHELON CANONICAL FORM 132
5.3 EXACT LIKELIHOOD FUNCTION FOR VECTOR ARMA MODELS 134 CONTENTS XV
5.3.1 EXPRESSIONS FOR THE EXACT LIKELIHOOD FUNCTION AND EXACT BACKCASTS
135 5.3.2 SPECIAL CASES OF THE EXACT LIKELIHOOD RESULTS 138 5.3.3 FINITE
SAMPLE FORECAST RESULTS BASED ON THE EXACT LIKELIHOOD APPROACH 140 5.4
INNOVATIONS FORM OF THE EXACT LIKELIHOOD FUNCTION FOR ARMA MODELS 145
5.4.1 USE OF INNOVATIONS ALGORITHM APPROACH FOR THE EXACT LIKELIHOOD 145
5.4.2 PREDICTION OF VECTOR ARMA PROCESSES USING THE INNOVATIONS APPROACH
. . 147 5.5 OVERALL CHECKING FOR MODEL ADEQUACY 149 5.5.1 RESIDUAL
CORRELATION MATRICES AND OVERALL GOODNESS-OF- FIT TEST 149 5.5.2
ASYMPTOTIC DISTRIBUTION OF RESIDUAL COVARIANCES AND GOODNESS-OF-FIT
STATISTIC 150 5.5.3 USE OF THE SCORE TEST STATISTIC FOR MODEL DIAGNOSTIC
CHECKING 151 5.6 EFFECTS OF PARAMETER ESTIMATION ERRORS ON PREDICTION
PROPERTIES 155 5.6.1 EFFECTS OF PARAMETER ESTIMATION ERRORS ON
FORECASTING IN THE VECTOR AR(P) MODEL 156 5.6.2 PREDICTION THROUGH
APPROXIMATION BY AUTOREGRESSIVE MODEL FITTING 158 5.7 MOTIVATION FOR AIC
AS CRITERION FOR MODEL SELECTION, AND CORRECTED VERSIONS OF AIC 160 5.8
NUMERICAL EXAMPLES 163 6. REDUCED-RANK AND NONSTATIONARY COINTEGRATED
MODELS 175 6.1 NESTED REDUCED-RANK AR MODELS AND PARTIAL CANONICAL
CORRELATION ANALYSIS 175 6.1.1 SPECIFICATION OF RANKS THROUGH PARTIAL
CANONICAL CORRELATION ANALYSIS 176 6.1.2 CANONICAL FORM FOR THE
REDUCED-RANK MODEL 178 6.1.3 MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS
IN THE MODEL 179 6.1.4 RELATION OF REDUCED-RANK AR MODEL WITH SCALAR
COMPONENT MODELS AND KRONECKER INDICES 181 6.2 REVIEW OF ESTIMATION AND
TESTING FOR NONSTATIONARITY (UNIT ROOTS) IN UNIVARIATE ARIMA MODELS 183
6.2.1 LIMITING DISTRIBUTION RESULTS IN THE AR(1) MODEL WITH A UNIT ROOT
183 XVI CONTENTS 6.2.2 UNIT-ROOT DISTRIBUTION RESULTS FOR GENERAL ORDER
AR MODELS 185 6.3 NONSTATIONARY (UNIT-ROOT) MULTIVARIATE AR MODELS,
ESTIMATION, AND TESTING 189 6.3.1 UNIT-ROOT NONSTATIONARY VECTOR AR
MODEL, THE ERROR- CORRECTION FORM, AND COINTEGRATION 189 6.3.2
ASYMPTOTIC PROPERTIES OF THE LEAST SQUARES ESTIMATOR 192 6.3.3
REDUCED-RANK ESTIMATION OF THE ERROR-CORRECTION FORM OF THE MODEL 194
6.3.4 LIKELIHOOD RATIO TEST FOR THE NUMBER OF UNIT ROOTS 199 6.3.5
REDUCED-RANK ESTIMATION THROUGH PARTIAL CANONICAL CORRELATION ANALYSIS
202 6.3.6 EXTENSION TO ACCOUNT FOR A CONSTANT TERM IN THE ESTIMATION 203
6.3.7 FORECAST PROPERTIES FOR THE COINTEGRATED MODEL 209 6.3.8 EXPLICIT
UNIT-ROOT STRUCTURE OF THE NONSTATIONARY AR MODEL AND IMPLICATIONS 210
6.3.9 FURTHER NUMERICAL EXAMPLES 212 6.4 A CANONICAL ANALYSIS FOR VECTOR
AUTOREGRESSIVE TIME SERIES 215 6.4.1 CANONICAL ANALYSIS BASED ON MEASURE
OF PREDICTABILITY 216 6.4.2 APPLICATION TO THE ANALYSIS OF NONSTATIONARY
SERIES FOR COINTEGRATION 218 6.5 MULTIPLICATIVE SEASONAL VECTOR ARMA
MODELS 219 6.5.1 SOME SPECIAL SEASONAL ARMA MODELS FOR VECTOR TIME
SERIES 220 7. STATE-SPACE MODELS, KALMAN FILTERING, AND RELATED TOPICS
226 7.1 STATE-VARIABLE MODELS AND KALMAN FILTERING 226 7.1.1 THE KALMAN
FILTERING RELATIONS 227 7.1.2 SMOOTHING RELATIONS IN THE STATE-VARIABLE
MODEL 230 7.1.3 INNOVATIONS FORM OF STATE-SPACE MODEL AND STEADY STATE
FOR TIME-INVARIANT MODELS 231 7.1.4 CONTROLLABILITY, OBSERVABILITY, AND
MINIMALITY FOR TIME-INVARIANT MODELS 232 7.2 STATE-VARIABLE
REPRESENTATIONS OF THE VECTOR ARMA MODEL 236 7.2.1 A STATE-SPACE FORM
BASED ON THE PREDICTION SPACE OF FUTURE VALUES 236 7.2.2 EXACT
LIKELIHOOD FUNCTION THROUGH THE STATE-VARIABLE APPROACH 237 7.2.3
ALTERNATE STATE-SPACE FORMS FOR THE VECTOR ARMA MODEL.. 242 CONTENTS
XVII 7.2.4 MINIMAL DIMENSION STATE-VARIABLE REPRESENTATION AND KRONECKER
INDICES 247 7.2.5 (MINIMAL DIMENSION) ECHELON CANONICAL STATE-SPACE
REPRESENTATION 247 7.3 EXACT LIKELIHOOD ESTIMATION FOR VECTOR ARMA
PROCESSES WITH MISSING VALUES 255 7.3.1 STATE-SPACE MODEL AND KALMAN
FILTERING WITH MISSING VALUES 255 7.3.2 ESTIMATION OF MISSING VALUES IN
ARMA MODELS 257 7.3.3 INITIALIZATION FOR KALMAN FILTERING, SMOOTHING,
AND LIKELIHOOD EVALUATION IN NONSTATIONARY MODELS 260 7.4 CLASSICAL
APPROACH TO SMOOTHING AND FILTERING OF TIME SERIES .. 265 7.4.1
SMOOTHING FOR UNIVARIATE TIME SERIES 266 7.4.2 SMOOTHING RELATIONS FOR
THE SIGNAL PLUS NOISE OR STRUCTURAL COMPONENTS MODEL 269 7.4.3 A SIMPLE
VECTOR STRUCTURAL COMPONENT MODEL FOR TREND 272 8. LINEAR MODELS WITH
EXOGENOUS VARIABLES 274 8.1 REPRESENTATIONS OF LINEAR MODELS WITH
EXOGENOUS VARIABLES 274 8.2 FORECASTING IN ARMAX MODELS 276 8.2.1
FORECASTS WHEN FUTURE EXOGENOUS VARIABLES MUST BE FORECASTED 276 8.2.2
MSE MATRIX OF OPTIMAL FORECASTS 278 8.2.3 FORECASTING WHEN FUTURE
EXOGENOUS VARIABLES ARE SPECIFIED 279 8.3 OPTIMAL FEEDBACK CONTROL IN
ARMAX MODELS 280 8.4 MODEL SPECIFICATION, ML ESTIMATION, AND MODEL
CHECKING FOR ARMAX MODELS 285 8.4.1 SOME COMMENTS ON SPECIFICATION AND
CHECKING OF ARMAX MODELS 285 8.4.2 ML ESTIMATION FOR ARMAX MODELS 286
8.4.3 ASYMPTOTIC DISTRIBUTION THEORY OF ESTIMATORS IN ARMAX MODELS 289
8.5 NUMERICAL EXAMPLE 292 APPENDIX: TIME SERIES DATA SETS 299 EXERCISES
AND PROBLEMS 315 REFERENCES 332 SUBJECT INDEX 345 AUTHOR INDEX 354
|
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| author | Reinsel, Gregory C. 1948-2004 |
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| classification_tum | MAT 634f MAT 627f |
| ctrlnum | (OCoLC)76551724 (DE-599)BVBBV019315975 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| id | DE-604.BV019315975 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:29Z |
| institution | BVB |
| isbn | 0387406190 9780387406190 |
| language | English |
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| spelling | Reinsel, Gregory C. 1948-2004 Verfasser (DE-588)113599382 aut Elements of multivariate time series analysis Gregory C. Reinsel 2. ed. New York [u.a.] Springer 2003 XVII, 357 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 332 - 344 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012783524&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reinsel, Gregory C. 1948-2004 Elements of multivariate time series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4040708-1 |
| title | Elements of multivariate time series analysis |
| title_auth | Elements of multivariate time series analysis |
| title_exact_search | Elements of multivariate time series analysis |
| title_full | Elements of multivariate time series analysis Gregory C. Reinsel |
| title_fullStr | Elements of multivariate time series analysis Gregory C. Reinsel |
| title_full_unstemmed | Elements of multivariate time series analysis Gregory C. Reinsel |
| title_short | Elements of multivariate time series analysis |
| title_sort | elements of multivariate time series analysis |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Zeitreihenanalyse Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012783524&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT reinselgregoryc elementsofmultivariatetimeseriesanalysis |