Smoothness Priors Analysis of Time Series

  • Genshiro Kitagawa
  • Will Gersch

Part of the Lecture Notes in Statistics book series (LNS, volume 116)

Table of contents

  1. Front Matter
    Pages i-x
  2. Genshiro Kitagawa, Will Gersch
    Pages 1-8
  3. Genshiro Kitagawa, Will Gersch
    Pages 9-26
  4. Genshiro Kitagawa, Will Gersch
    Pages 27-32
  5. Genshiro Kitagawa, Will Gersch
    Pages 33-53
  6. Genshiro Kitagawa, Will Gersch
    Pages 55-65
  7. Genshiro Kitagawa, Will Gersch
    Pages 67-89
  8. Genshiro Kitagawa, Will Gersch
    Pages 91-104
  9. Genshiro Kitagawa, Will Gersch
    Pages 105-121
  10. Genshiro Kitagawa, Will Gersch
    Pages 123-135
  11. Genshiro Kitagawa, Will Gersch
    Pages 137-145
  12. Genshiro Kitagawa, Will Gersch
    Pages 147-160
  13. Genshiro Kitagawa, Will Gersch
    Pages 161-179
  14. Genshiro Kitagawa, Will Gersch
    Pages 181-187
  15. Genshiro Kitagawa, Will Gersch
    Pages 189-200
  16. Genshiro Kitagawa, Will Gersch
    Pages 201-212
  17. Genshiro Kitagawa, Will Gersch
    Pages 213-230
  18. Back Matter
    Pages 231-263

About this book

Introduction

Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.

Keywords

Likelihood Smooth function Time series Variance calculus classification data analysis differential equation maximum measure

Authors and affiliations

  • Genshiro Kitagawa
    • 1
  • Will Gersch
    • 2
  1. 1.The Institute of Statistical MathematicsTokyoJapan
  2. 2.Department of Information and Computer ScienceUniversity of HawaiiHonoluluUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0761-0
  • Copyright Information Springer-Verlag New York, Inc. 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94819-5
  • Online ISBN 978-1-4612-0761-0
  • Series Print ISSN 0930-0325
  • About this book