Elements of multivariate time series analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1993
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 263 S. graph. Darst. |
| ISBN: | 0387940634 3540940634 |
Staff View
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Record in the Search Index
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| adam_text |
GREGORY C. REINSEL
ELEMENTS OF MULTIVARIATE
TIME
SERIES ANALYSIS
WITH
11
ILLUSTRATIONS
SPRINGER-VERLAG
NEW
YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONG KONG BARCELONA BUDAPEST
CONTENTS
PREFACE VII
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 EXPECTED VALUES AND COVARIANCE MATRICES OF RANDOM
VECTORS
13
A1.3 THE MULTIVARIATE NORMAL DISTRIBUTION 14
A1.4 SOME BASIC RESULTS ON STOCHASTIC CONVERGENCE 18
2.
VECTOR ARMA TIME SERIES MODELS AND FORECASTING 21
2.1 VECTOR MOVING AVERAGE MODELS 21
2.1.1 INVERTIBILITY OF THE VECTOR MOVING AVERAGE MODEL 21
2.1.2
COVARIANCE MATRICES OF THE VECTOR MOVING AVERAGE
MODEL
22
2.1.3 FEATURES OF THE VECTOR MA(1) MODEL 23
CONTENTS
2.1.4 MODEL STRUCTURE FOR SUBSET OF COMPONENTS IN THE VECTOR
MA
MODEL 24
2.2 VECTOR AUTOREGRESSIVE MODELS 26
2.2.1 STATIONARITY OF THE VECTOR AUTOREGRESSIVE MODEL 26
2.2.2 YULE-WALKER RELATIONS FOR COVARIANCE MATRICES OF A
VECTOR
AR PROCESS 28
2.2.3 COVARIANCE FEATURES OF THE VECTOR AR(1) MODEL 28
2.2.4 UNIVARIATE MODEL STRUCTURE IMPLIED BY VECTOR AR MODEL . 29
2.3
VECTOR MIXED AUTOREGRESSIVE MOVING AVERAGE MODELS 33
2.3.1
STATIONARITY AND INVERTIBILITY OF THE VECTOR ARMA MODEL. 33
2.3.2
RELATIONS FOR THE COVARIANCE MATRICES OF THE VECTOR
ARMA MODEL 34
2.3.3 SOME FEATURES OF THE VECTOR ARMA( 1,1) MODEL 35
2.3.4 CONSIDERATION OF PARAMETER IDENTIFIABILITY FOR VECTOR
ARMA
MODELS 36
2.3.5 FURTHER ASPECTS OF NONUNIQUENESS OF VECTOR ARMA
MODEL
REPRESENTATIONS 39
2.4 NONSTATIONARY VECTOR ARMA MODELS 40
2.4.1 VECTOR ARIMA MODELS FOR NONSTATIONARY PROCESSES 41
2.4.2
COINTEGRATION IN NONSTATIONARY VECTOR PROCESSES 42
2.4.3
THE VECTOR IMA(1,1) PROCESS OR EXPONENTIAL SMOOTHING
MODEL
: 43
2.5 PREDICTION FOR VECTOR ARMA MODELS 45
2.5.1 MINIMUM MEAN SQUARED ERROR PREDICTION 46
2.5.2 FORECASTING FOR VECTOR ARMA PROCESSES AND COVARIANCE
MATRICES
OF FORECAST ERRORS 46
2.5.3 COMPUTATION OF FORECASTS FOR VECTOR ARMA PROCESSES 48
2.5.4
SOME EXAMPLES OF FORECAST FUNCTIONS FOR VECTOR ARMA
MODELS
49
. CANONICAL STRUCTURE OF VECTOR ARMA MODELS 52
3.1 CONSIDERATION OF KRONECKER STRUCTURE FOR VECTOR ARMA -S
MODELS
52
3.1.1 KRONECKER INDICES AND MCMILLAN DEGREE OF VECTOR
ARMA
PROCESS 53
3.1.2 ECHELON FORM STRUCTURE OF VECTOR ARMA MODEL IMPLIED
BY
KRONECKER INDICES 54
3.1.3 REDUCED-RANK FORM OF VECTOR ARMA MODEL IMPLIED BY
KRONECKER
INDICES 56
3.2 CANONICAL CORRELATION STRUCTURE FOR ARMA TIME SERIES 58
3.2.1
CANONICAL CORRELATIONS FOR VECTOR ARMA PROCESSES 60
3.2.2
RELATION TO SCALAR COMPONENT MODEL STRUCTURE 61
1
CONTENTS XI
3.3 PARTIAL AUTOREGRESSIVE AND PARTIAL CORRELATION MATRICES 64
3.3.1
VECTOR AUTOREGRESSIVE MODEL APPROXIMATIONS AND PARTIAL
AUTOREGRESSION
MATRICES 64
3.3.2 RECURSIVE FITTING OF VECTOR AR MODEL APPROXIMATIONS 66
3.3.3
PARTIAL CROSS-CORRELATION MATRICES FOR A STATIONARY VECTOR
PROCESS
69
3.3.4 PARTIAL CANONICAL CORRELATIONS FOR A STATIONARY VECTOR
PROCESS
71
4.
INITIAL MODEL BUILDING AND LEAST SQUARES ESTIMATION FOR VECTOR AR
MODELS
74
4.1 SAMPLE CROSS-COVARIANCE AND CORRELATION MATRICES AND THEIR
PROPERTIES
74
4.1.1 SAMPLE ESTIMATES OF MEAN VECTOR AND OF COVARIANCE AND
CORRELATION
MATRICES 74
4.1.2 ASYMPTOTIC PROPERTIES OF SAMPLE CORRELATIONS 76
4.2 SAMPLE PARTIAL AR AND PARTIAL CORRELATION MATRICES AND THEIR
PROPERTIES
78
4.2.1 TEST FOR ORDER OF AR MODEL BASED ON SAMPLE PARTIAL
AUTOREGRESSION
MATRICES 78
4.2.2 EQUIVALENT TEST STATISTICS BASED ON SAMPLE PARTIAL
CORRELATION
MATRICES 79
4.3 CONDITIONAL LEAST SQUARES ESTIMATION OF VECTOR AR MODELS 80
4.3.1
LEAST SQUARES ESTIMATION FOR THE VECTOR AR(1) MODEL 81
4.3.2
LEAST SQUARES ESTIMATION FOR THE VECTOR AR MODEL OF
GENERAL
ORDER 83
4.3.3 LIKELIHOOD RATIO TESTING FOR THE ORDER OF THE AR MODEL 85
4.3.4
DERIVATION OF THE WALD STATISTIC FOR TESTING THE ORDER OF
THE
AR MODEL 85
4.4 RELATION OF LSE TO YULE-WALKER ESTIMATE FOR VECTOR AR
MODELS
89
4.5 ADDITIONAL TECHNIQUES FOR SPECIFICATION OF VECTOR ARMA
MODELS
91
4.5.1 USE OF ORDER SELECTION CRITERIA FOR MODEL SPECIFICATION 92
4.5.2
SAMPLE CANONICAL CORRELATION ANALYSIS METHODS 93
4.5.3
ORDER DETERMINATION USING LINEAR LSE METHODS FOR THE
VECTOR
ARMA MODEL 96
A4 APPENDIX: REVIEW OF THE GENERAL MULTIVARIATE LINEAR
REGRESSION
MODEL 105
A4.1 PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE
REGRESSION
MATRIX 105
A4.2 LIKELIHOOD RATIO TEST OF LINEAR HYPOTHESIS ABOUT
REGRESSION
COEFFICIENTS 107
XII CONTENTS
A4.3 ASYMPTOTICALLY EQUIVALENT FORMS OF THE TEST OF LINEAR
HYPOTHESIS
108
5.
MAXIMUM LIKELIHOOD ESTIMATION AND MODEL CHECKING FOR VECTOR
ARMA MODELS 111
5.1 CONDITIONAL MAXIMUM LIKELIHOOD ESTIMATION FOR VECTOR
ARMA
MODELS 111
5.1.1 CONDITIONAL LIKELIHOOD FUNCTION FOR THE VECTOR ARMA
MODEL
112
5.1.2 LIKELIHOOD EQUATIONS FOR CONDITIONAL ML ESTIMATION 113
5.1.3
ITERATIVE COMPUTATION OF THE CONDITIONAL MLE BY GLS
ESTIMATION
115
5.1.4 ASYMPTOTIC DISTRIBUTION FOR THE MLE IN THE VECTOR
ARMA
MODEL 117
5.2 ML ESTIMATION AND LR TESTING OF ARMA MODELS UNDER
LINEAR
RESTRICTIONS 118
5.2.1 ML ESTIMATION OF VECTOR ARMA MODELS WITH LINEAR
CONSTRAINTS
ON THE PARAMETERS 118
5.2.2 LR TESTING OF THE HYPOTHESIS OF THE LINEAR CONSTRAINTS 120
5.2.3
ML ESTIMATION OF VECTOR ARMA MODELS IN THE ECHELON
CANONICAL
FORM 121
5.3 EXACT LIKELIHOOD FUNCTION FOR VECTOR ARMA MODELS 122
5.3.1
EXPRESSIONS FOR THE EXACT LIKELIHOOD FUNCTION AND EXACT
BACKCASTS
124
5.3.2 SPECIAL CASES OF THE EXACT LIKELIHOOD RESULTS 126
5.4 INNOVATIONS FORM OF THE EXACT LIKELIHOOD FUNCTION FOR
ARMA
MODELS 129
5.4.1 USE OF INNOVATIONS ALGORITHM APPROACH FOR THE EXACT
LIKELIHOOD
129
5.4.2 PREDICTION OF VECTOR ARMA PROCESSES USING THE
INNOVATIONS
APPROACH 131
5.5 OVERALL CHECKING FOR MODEL ADEQUACY 132
5.5.1 RESIDUAL CORRELATION MATRICES, AND OVERALL
GOODNESS-OF
FIT
TEST 132
5.5.2 ASYMPTOTIC DISTRIBUTION OF RESIDUAL COVARIANCES AND
GOODNESS-OF-FIT
STATISTIC 133
5.5.3 USE OF THE SCORE TEST STATISTIC FOR MODEL DIAGNOSTIC
CHECKING
134
5.6 EFFECTS OF PARAMETER ESTIMATION ERRORS ON PREDICTION
PROPERTIES
138
5.6.1 EFFECTS OF PARAMETER ESTIMATION ERRORS ON FORECASTING IN
THE
VECTOR AR(P) MODEL 139
CONTENTS XIII
5.6.2 PREDICTION THROUGH APPROXIMATION BY AUTOREGRESSIVE
MODEL
FITTING 141
5.7 NUMERICAL EXAMPLES 142
6. REDUCED-RANK AND NONSTATIONARY CO-INTEGRATED MODELS 154
6.1 NESTED REDUCED-RANK AR MODELS AND PARTIAL CANONICAL
CORRELATION
ANALYSIS 154
6.1.1 SPECIFICATION OF RANKS THROUGH PARTIAL CANONICAL
CORRELATION
ANALYSIS 155
6.1.2 CANONICAL FORM FOR THE REDUCED-RANK MODEL 157
6.1.3 MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS IN THE
MODEL
158
6.1.4 RELATION OF REDUCED-RANK AR MODEL WITH SCALAR
COMPONENT
MODELS AND KRONECKER INDICES
'.
159
6.2
REVIEW OF ESTIMATION AND TESTING FOR NONSTATIONARITY (UNIT
ROOTS)
IN UNIVARIATE ARIMA MODELS 162
6.2.1 LIMITING DISTRIBUTION RESULTS IN THE AR(1) MODEL WITH A
UNIT
ROOT 162
6.2.2 UNIT-ROOT DISTRIBUTION RESULTS FOR GENERAL ORDER AR
MODELS
163
6.3 NONSTATIONARY (UNIT-ROOT) MULTIVARIATE AR MODELS,
ESTIMATION,
AND TESTING 165
6.3.1 UNIT-ROOT NONSTATIONARY VECTOR AR MODEL, AND THE
ERROR-CORRECTION
FORM 165
6.3.2 ASYMPTOTIC PROPERTIES OF THE LEAST SQUARES ESTIMATOR 166
6.3.3
REDUCED-RANK ESTIMATION OF THE ERROR-CORRECTION FORM
OF
THE MODEL 169
6.3.4 LIKELIHOOD RATIO TEST FOR THE NUMBER OF UNIT ROOTS 172
6.3.5
REDUCED-RANK ESTIMATION THROUGH PARTIAL CANONICAL
CORRELATION
ANALYSIS 174
6.3.6 EXTENSION TO ACCOUNT FOR A CONSTANT TERM IN THE
ESTIMATION
175
6.3.7 FORECAST PROPERTIES FOR THE CO-INTEGRATED MODEL 180
6.3.8
EXPLICIT UNIT-ROOT STRUCTURE OF THE NONSTATIONARY AR
MODEL
AND IMPLICATIONS 181
6.3.9 FURTHER NUMERICAL EXAMPLES 183
6.4 MULTIPLICATIVE SEASONAL VECTOR ARMA MODELS 186
6.4.1 SOME SPECIAL SEASONAL ARMA MODELS FOR VECTOR TIME
SERIES
187
7.
STATE-SPACE MODELS, KALMAN FILTERING, AND RELATED TOPICS 192
7.1 STATE-VARIABLE MODELS AND KALMAN FILTERING 192 |
| any_adam_object | 1 |
| author | Reinsel, Gregory C. 1948-2004 |
| author_GND | (DE-588)113599382 |
| author_facet | Reinsel, Gregory C. 1948-2004 |
| author_role | aut |
| author_sort | Reinsel, Gregory C. 1948-2004 |
| author_variant | g c r gc gcr |
| building | Verbundindex |
| bvnumber | BV008380894 |
| callnumber-first | Q - Science |
| callnumber-label | QA280 |
| callnumber-raw | QA280.R45 1995 |
| callnumber-search | QA280.R45 1995 |
| callnumber-sort | QA 3280 R45 41995 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)263299631 (DE-599)BVBBV008380894 |
| dewey-full | 519.5/520 519.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 20 519.55 |
| dewey-search | 519.5/5 20 519.55 |
| dewey-sort | 3519.5 15 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV008380894 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T09:01:50Z |
| institution | BVB |
| isbn | 0387940634 3540940634 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005526518 |
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| physical | XIV, 263 S. graph. Darst. |
| publishDate | 1993 |
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| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Reinsel, Gregory C. 1948-2004 Verfasser (DE-588)113599382 aut Elements of multivariate time series analysis Gregory C. Reinsel New York u.a. Springer 1993 XIV, 263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Multivariate analyse gtt Tijdreeksen gtt Time-series analysis Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Multivariate Analyse (DE-588)4040708-1 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005526518&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 Multivariate analyse gtt Tijdreeksen gtt Time-series analysis Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4067486-1 |
| 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 | Multivariate analyse gtt Tijdreeksen gtt Time-series analysis Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Multivariate analyse Tijdreeksen Time-series analysis Multivariate analysis Multivariate Analyse Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005526518&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT reinselgregoryc elementsofmultivariatetimeseriesanalysis |