Skip to main content
  • Book
  • © 1987

State Space Modeling of Time Series

Authors:

(view affiliations)

Part of the book series: Universitext (UTX)

Buying options

eBook
USD 74.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-96985-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout

This is a preview of subscription content, access via your institution.

Table of contents (14 chapters)

  1. Front Matter

    Pages I-XI
  2. Introduction

    • Masanao Aoki
    Pages 1-2
  3. The Notion of State

    • Masanao Aoki
    Pages 3-8
  4. Representation of Time Series

    • Masanao Aoki
    Pages 9-29
  5. State Space and ARMA Representation

    • Masanao Aoki
    Pages 30-57
  6. Properties of State Space Models

    • Masanao Aoki
    Pages 58-84
  7. Innovation Processes

    • Masanao Aoki
    Pages 85-89
  8. Kalman Filters

    • Masanao Aoki
    Pages 90-110
  9. State Vectors and Optimality Measures

    • Masanao Aoki
    Pages 111-118
  10. Computation of System Matrices

    • Masanao Aoki
    Pages 119-148
  11. Approximate Models and Error Analysis

    • Masanao Aoki
    Pages 149-176
  12. Numerical Examples

    • Masanao Aoki
    Pages 177-228
  13. Erratum to: Computation of System Matrices

    • Masanao Aoki
    Pages 315-315
  14. Erratum

    • Masanao Aoki
    Pages 315-315
  15. Back Matter

    Pages 229-314

About this book

model's predictive capability? These are some of the questions that need to be answered in proposing any time series model construction method. This book addresses these questions in Part II. Briefly, the covariance matrices between past data and future realizations of time series are used to build a matrix called the Hankel matrix. Information needed for constructing models is extracted from the Hankel matrix. For example, its numerically determined rank will be the di­ mension of the state model. Thus the model dimension is determined by the data, after balancing several sources of error for such model construction. The covariance matrix of the model forecasting error vector is determined by solving a certain matrix Riccati equation. This matrix is also the covariance matrix of the innovation process which drives the model in generating model forecasts. In these model construction steps, a particular model representation, here referred to as balanced, is used extensively. This mode of model representation facilitates error analysis, such as assessing the error of using a lower dimensional model than that indicated by the rank of the Hankel matrix. The well-known Akaike's canonical correlation method for model construc­ tion is similar to the one used in this book. There are some important differ­ ences, however. Akaike uses the normalized Hankel matrix to extract canonical vectors, while the method used in this book does not normalize the Hankel ma­ trix.

Keywords

  • Instrumental variables
  • Instrumentalvariablen
  • Time series
  • Zeitreihe
  • algorithms
  • dynamic programming
  • forecasting
  • information
  • innovation
  • modeling
  • optimization
  • rating
  • regression
  • value-at-risk

Authors and Affiliations

  • Department of Computer Science and Department of Economics, University of California, Los Angeles, USA

    Masanao Aoki

Bibliographic Information

  • Book Title: State Space Modeling of Time Series

  • Authors: Masanao Aoki

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-642-96985-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • eBook ISBN: 978-3-642-96985-0

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XI, 315

  • Topics: Quantitative Economics, Operations Research and Decision Theory

Buying options

eBook
USD 74.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-96985-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout