State Space Modeling of Time Series

Authors: Prof. Masanao Aoki



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.

Table of contents

Front Matter
Pages I-XVII

Pages 1-2
Introduction

Pages 3-7
The Notion of State

Pages 8-20
Data Generating Processes

Pages 21-38
State Space and ARMA Models

Pages 39-49
Properties of State Space Models

Pages 50-70
Hankel Matrix and Singular Value Decomposition

Pages 71-98
Innovation Models, Riccati Equations, and Multiplier Analysis

Pages 99-104
State Vectors and Optimality Measures

Pages 105-164
Estimation of System Matrices

Pages 165-186
Approximate Models and Error Analysis

Pages 187-228
Integrated Time Series

Pages 229-248
Numerical Examples

Back Matter
Pages 249-326