Smoothness Priors Analysis of Time Series

1. Front Matter

   Pages i-x

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2. Introduction

   • Genshiro Kitagawa, Will Gersch

   Pages 1-8

3. Modeling Concepts and Methods

   • Genshiro Kitagawa, Will Gersch

   Pages 9-26

4. The Smoothness Priors Concept

   • Genshiro Kitagawa, Will Gersch

   Pages 27-32

5. Scalar Least Squares Modeling

   • Genshiro Kitagawa, Will Gersch

   Pages 33-53

6. Linear Gaussian State Space Modeling

   • Genshiro Kitagawa, Will Gersch

   Pages 55-65

7. General State Space Modeling

   • Genshiro Kitagawa, Will Gersch

   Pages 67-89

8. Applications of Linear Gaussian State Space Modeling

   • Genshiro Kitagawa, Will Gersch

   Pages 91-104

9. Modeling Trends

   • Genshiro Kitagawa, Will Gersch

   Pages 105-121

10. Seasonal Adjustment

    • Genshiro Kitagawa, Will Gersch

    Pages 123-135

11. Estimation of Time Varying Variance

    • Genshiro Kitagawa, Will Gersch

    Pages 137-145

12. Modeling Scalar Nonstationary Covariance Time Series

    • Genshiro Kitagawa, Will Gersch

    Pages 147-160

13. Modeling Multivariate Nonstationary Covariance Time Series

    • Genshiro Kitagawa, Will Gersch

    Pages 161-179

14. Modeling Inhomogeneous Discrete Processes

    • Genshiro Kitagawa, Will Gersch

    Pages 181-187

15. Quasi-Periodic Process Modeling

    • Genshiro Kitagawa, Will Gersch

    Pages 189-200

16. Nonlinear Smoothing

    • Genshiro Kitagawa, Will Gersch

    Pages 201-212

17. Other Applications

    • Genshiro Kitagawa, Will Gersch

    Pages 213-230

18. Back Matter

    Pages 231-263

    PDF

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.

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

• The Institute of Statistical Mathematics, Tokyo, Japan

  Genshiro Kitagawa

• Department of Information and Computer Science, University of Hawaii, Honolulu, USA

  Will Gersch

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