Ebook: State Space Modeling of Time Series

In this book, the author adopts a state space approach to time series modeling to provide a new, computer-oriented method for building models for vector-valued time series. This second edition has been completely reorganized and rewritten. Background material leading up to the two types of estimators of the state space models is collected and presented coherently in four consecutive chapters. New, fuller descriptions are given of state space models for autoregressive models commonly used in the econometric and statistical literature. Backward innovation models are newly introduced in this edition in addition to the forward innovation models, and both are used to construct instrumental variable estimators for the model matrices. Further new items in this edition include statistical properties of the two types of estimators, more details on multiplier analysis and identification of structural models using estimated models, incorporation of exogenous signals and choice of model size. A whole new chapter is devoted to modeling of integrated, nearly integrated and co-integrated time series.

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In this book, the author adopts a state space approach to time series modeling to provide a new, computer-oriented method for building models for vector-valued time series. This second edition has been completely reorganized and rewritten. Background material leading up to the two types of estimators of the state space models is collected and presented coherently in four consecutive chapters. New, fuller descriptions are given of state space models for autoregressive models commonly used in the econometric and statistical literature. Backward innovation models are newly introduced in this edition in addition to the forward innovation models, and both are used to construct instrumental variable estimators for the model matrices. Further new items in this edition include statistical properties of the two types of estimators, more details on multiplier analysis and identification of structural models using estimated models, incorporation of exogenous signals and choice of model size. A whole new chapter is devoted to modeling of integrated, nearly integrated and co-integrated time series.

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In this book, the author adopts a state space approach to time series modeling to provide a new, computer-oriented method for building models for vector-valued time series. This second edition has been completely reorganized and rewritten. Background material leading up to the two types of estimators of the state space models is collected and presented coherently in four consecutive chapters. New, fuller descriptions are given of state space models for autoregressive models commonly used in the econometric and statistical literature. Backward innovation models are newly introduced in this edition in addition to the forward innovation models, and both are used to construct instrumental variable estimators for the model matrices. Further new items in this edition include statistical properties of the two types of estimators, more details on multiplier analysis and identification of structural models using estimated models, incorporation of exogenous signals and choice of model size. A whole new chapter is devoted to modeling of integrated, nearly integrated and co-integrated time series.
Content:
Front Matter....Pages I-XVII
Introduction....Pages 1-2
The Notion of State....Pages 3-7
Data Generating Processes....Pages 8-20
State Space and ARMA Models....Pages 21-38
Properties of State Space Models....Pages 39-49
Hankel Matrix and Singular Value Decomposition....Pages 50-70
Innovation Models, Riccati Equations, and Multiplier Analysis....Pages 71-98
State Vectors and Optimality Measures....Pages 99-104
Estimation of System Matrices....Pages 105-164
Approximate Models and Error Analysis....Pages 165-186
Integrated Time Series....Pages 187-228
Numerical Examples....Pages 229-248
Back Matter....Pages 249-326

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In this book, the author adopts a state space approach to time series modeling to provide a new, computer-oriented method for building models for vector-valued time series. This second edition has been completely reorganized and rewritten. Background material leading up to the two types of estimators of the state space models is collected and presented coherently in four consecutive chapters. New, fuller descriptions are given of state space models for autoregressive models commonly used in the econometric and statistical literature. Backward innovation models are newly introduced in this edition in addition to the forward innovation models, and both are used to construct instrumental variable estimators for the model matrices. Further new items in this edition include statistical properties of the two types of estimators, more details on multiplier analysis and identification of structural models using estimated models, incorporation of exogenous signals and choice of model size. A whole new chapter is devoted to modeling of integrated, nearly integrated and co-integrated time series.
Content:
Front Matter....Pages I-XVII
Introduction....Pages 1-2
The Notion of State....Pages 3-7
Data Generating Processes....Pages 8-20
State Space and ARMA Models....Pages 21-38
Properties of State Space Models....Pages 39-49
Hankel Matrix and Singular Value Decomposition....Pages 50-70
Innovation Models, Riccati Equations, and Multiplier Analysis....Pages 71-98
State Vectors and Optimality Measures....Pages 99-104
Estimation of System Matrices....Pages 105-164
Approximate Models and Error Analysis....Pages 165-186
Integrated Time Series....Pages 187-228
Numerical Examples....Pages 229-248
Back Matter....Pages 249-326
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