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State Space Modeling of Time Series

  • Masanao Aoki

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Masanao Aoki
    Pages 1-2
  3. Masanao Aoki
    Pages 3-8
  4. Masanao Aoki
    Pages 9-29
  5. Masanao Aoki
    Pages 30-57
  6. Masanao Aoki
    Pages 58-84
  7. Masanao Aoki
    Pages 85-89
  8. Masanao Aoki
    Pages 90-110
  9. Masanao Aoki
    Pages 111-118
  10. Masanao Aoki
    Pages 119-148
  11. Masanao Aoki
    Pages 149-176
  12. Masanao Aoki
    Pages 177-228
  13. Masanao Aoki
    Pages 315-315
  14. Masanao Aoki
    Pages 315-315
  15. Back Matter
    Pages 229-314

About this book

Introduction

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

  • Masanao Aoki
    • 1
  1. 1.Department of Computer Science and Department of EconomicsUniversity of CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-96985-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17257-4
  • Online ISBN 978-3-642-96985-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site