State space modeling of time series:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1990
|
| Edition: | 2., rev. and enl. ed. |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002115837&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 301 - 320 |
| Physical Description: | XVII, 323 S. graph. Darst. |
| ISBN: | 3540528695 0387528695 3540528709 0387528709 |
Staff View
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| 100 | 1 | |a Aoki, Masanao |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a State space modeling of time series |c Masanao Aoki |
| 250 | |a 2., rev. and enl. ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1990 | |
| 300 | |a XVII, 323 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| DE-BY-TUM_katkey | 491785 |
| DE-BY-TUM_location | Mag |
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| _version_ | 1821934770037194755 |
| adam_text | Masanao Aoki
State Space Modeling
of Time Series
Second, Revised and Enlarged Edition
With 13 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Contents
1 Introduction 1
2 The Notion of State 3
3 Data Generating Processes 8
3 1 Statistical Data Descriptions 9
3 2 Spectral Factorization 10
3 3 Decomposition of Time Series 12
Dynamic Modes 12
Two Aggregation Schemes 14
Unit Roots 17
Regime Shifts and Structural Changes 18
3 4 Minimum-Phase Transfer Function Representation 19
4 State Space and ARMA Models 21
4 1 State Space Models 21
4 2 Conversion to State Space Representation 22
Observability Canonical Form 23
Vector Models 32
Gilbert s Method 37
4 3 Conversion of State Space Models into ARMA Models 38
5 Properties of State Space Models 39
5 1 Observability 39
Observability and Consistency of Least Squares Estimates 40
Lyapunov Equations 41
5 2 Orthogonal Projections 42
Example: Kalman Filters 45
6 Hankel Matrix and Singular Value Decomposition 50
6 1 The Hankel Matrix 50
XIV
6 2 Singular Value Decomposition 54
Sensitivity of Singular Values 56
Rank and Singular Values 56
Approximate Regression Analysis 58
6 3 Balanced Realization of State Space Model 59
Effects of Scaling 63
Parametrization 65
6 4 Examples with Exact Covariance Matrices 66
6 5 Hankel Norm of a Transfer Function 68
6 6 Singular Value Decomposition in the z-Domain 68
7 Innovation Models, Riccati Equations, and Multiplier Analysis 71
7 1 Innovation Models 71
Forward Innovation Models 71
Backward Innovation Models 74
7 2 Solving Riccati Equations 76
Closed Form Solutions for VAR Models 77
Iterative Solution Algorithm 78
A Non-Iterative Solution Algorithm 79
7 3 Likelihood Functions 83
Identification 87
7 4 Dynamic Multiplier Analysis and Structural Model Identification 88
Confidence Interval of Impulse Response Analysis 88
Variance Decomposition 89
Identification Exercises 91
7 5 Out-of-Sample Forecasts 97
8 State Vectors and Optimality Measures 99
8 1 Canonical Variates 99
Mutual Information 100
8 2 Prediction Error 100
8 3 Singular Values and Canonical Correlation Coefficients 101
XV
9 Estimation of System Matrices 105
9 1 Two Classes of Estimators of System Matrices 105
Stochastic Realization Estimator 108
The Instrumental Variables Estimator 110
9 2 Properties of Balanced Models 112
Nesting of System Matrix Estimates and IT 112
Stability 114
9 3 Examples with Exact Covariance Matrices 116
Models for VAR Processes 119
Choices of K 126
Models for MA Processes 127
Models for Vector-Valued ARMA Processes 132
9 4 Numerical Examples 141
9 5 Monte Carlo Experiments 147
AR(1) Models 147
Experimental Results 151
AR(2) Models 152
9 6 Model Selection 157
Examples 159
9 7 Incorporating Exogenous Variables 160
Regression Model 160
Dynamic Model 161
10 Approximate Models and Error Analysis 165
10 1 Structural Sensitivity 165
10 2 Error Norms 171
10 3 Asymptotic Error Covariance Matrices of Estimators 177
Variances of A and Z 178
Errors of System Matrix Estimates 180
10 4 Other Statistical Aspects 183
Test for Residuals 183
Variability of Sample Correlation Coefficients 184
Variances of Sample Covariances 185
XVI
11 Integrated Time Series 187
11 1 The Beveridge and Nelson Decomposition 188
11 2 State Space Decomposition 191
11 3 Contents of Random Walk Components 193
11 4 Cointegration, Error Correction, and Dynamic Aggregation 196
11 5 Two-Step Modeling Procedure 199
First Step 200
Second Step 200
11 6 Dynamic Structure of Seasonal Components 202
11 7 Large Sample Properties 206
Drift Term 213
11 8 Drifts or Linear Deterministic Trends? 216
11 9 Regime Shifts 223
11 10 Nearly Integrated Processes 225
12 Numerical Examples 229
12 1 West Germany 229
12 2 United Kingdom 230
12 3 The United States of America 230
A Money Stock 230
Money Stock and CPI 231
US Consumer Price Index 232
Real GNP, CPI and M 2 234
12 4 The US and West German Real GNP Interaction 239
12 5 The US and West German Real GNP and Unemployment Rate 241
12 6 The US and Japan Real GNP Interaction 244
12 7 The USA, West Germany, and Japan Real GNP Interaction 246
12 8 Further Examples 246
XVII
Appendices 249
A I Geometry of Weakly Stationary Stochastic Sequences 251
A 2 The z-Transform 254
A 3 Discrete and Continuous Time System Correspondences 259
A 4 Some Useful Relations for Matrix Quadratic Forms 261
A 5 Computation of Sample Covariance Matrices 263
A 6 Properties of Symplectic Matrices 265
A 7 Common Factors in ARMA Models 270
A 8 Singular Value Decomposition Theorem 272
A 9 Hankel Matrices 274
A 10 Spectral Factorization 277
A 11 Time Series from Intertemporal Optimization 284
A 12 Time Series from Rational Expectations Models 292
A 13 Data Sources 300
References 301
Subject Index 321
|
| any_adam_object | 1 |
| author | Aoki, Masanao |
| author_facet | Aoki, Masanao |
| author_role | aut |
| author_sort | Aoki, Masanao |
| author_variant | m a ma |
| building | Verbundindex |
| bvnumber | BV003350380 |
| classification_rvk | QH 237 SK 845 |
| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)246694272 (DE-599)BVBBV003350380 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2., rev. and enl. ed. |
| format | Book |
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| id | DE-604.BV003350380 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:03:03Z |
| institution | BVB |
| isbn | 3540528695 0387528695 3540528709 0387528709 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002115837 |
| oclc_num | 246694272 |
| open_access_boolean | |
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| physical | XVII, 323 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Aoki, Masanao State space modeling of time series Zeitreihenanalyse (DE-588)4067486-1 gnd Zustandsraum (DE-588)4132647-7 gnd Modell (DE-588)4039798-1 gnd Zeitreihe (DE-588)4127298-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4132647-7 (DE-588)4039798-1 (DE-588)4127298-5 (DE-588)4123037-1 |
| title | State space modeling of time series |
| title_auth | State space modeling of time series |
| title_exact_search | State space modeling of time series |
| title_full | State space modeling of time series Masanao Aoki |
| title_fullStr | State space modeling of time series Masanao Aoki |
| title_full_unstemmed | State space modeling of time series Masanao Aoki |
| title_short | State space modeling of time series |
| title_sort | state space modeling of time series |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Zustandsraum (DE-588)4132647-7 gnd Modell (DE-588)4039798-1 gnd Zeitreihe (DE-588)4127298-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Zeitreihenanalyse Zustandsraum Modell Zeitreihe Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002115837&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT aokimasanao statespacemodelingoftimeseries |
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