Smoothness priors analysis of time series
type: Item
instance of: scholarly article
title: Smoothness priors analysis of time series
zbMATH Open document ID: 0853.62069
DOI: 10.1007/978-1-4612-0761-0
author: Will Gersch
author: Genshiro Kitagawa
published in: Lecture Notes in Statistics
publication date: 1996-09-16T00:00:00Z
review text: Originally smoothness priors was a least squares computational treatment of some time series. The treatment was based on linear model Gaussian stochastic regression. The authors extended the results to linear Gaussian state space smoothness priors modelling of time series. In this approach a prior distribution on coefficients of a model is parametrized by hyperparameters. If the number of hyperparameters is small then the maximization of the likelihood permits the robust modelling of a time series with a complex structure. The general approach is applied to seasonal time series, discrete time processes, quasi-periodic processes, nonlinear state estimation and smoothing, hidden Markov state classification procedures, and modelling data sets with missing data. Theoretical results are illustrated on numerical examples. The book contains the following chapters: 1. Introduction; 2. Modeling concepts and methods; 3. The smoothness prior concepts; 4. Scalar least squares modeling; 5. Linear Gaussian state space modeling; 6. General state space modeling; 7. Applications of linear Gaussian state space modeling; 8. Modeling trends; 9. Seasonal adjustment; 10. Estimation of time varying variance; 11. Modeling scalar nonstationary covariance time series; 12. Modeling multivariate nonstationary covariance time series; 13. Modeling inhomogeneous discrete processes; 14. Quasi-periodic process modeling; 15. Nonlinear smoothing; 16. Other applications.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 927555
zbMATH Keywords: general state space modeling
zbMATH Keywords: seasonal adjustment
zbMATH Keywords: nonlinear smoothing
zbMATH Keywords: smoothness priors
zbMATH Keywords: hyperparameters
zbMATH Keywords: seasonal time series
zbMATH Keywords: discrete time processes
zbMATH Keywords: quasi-periodic processes
zbMATH Keywords: nonlinear state estimation
zbMATH Keywords: hidden Markov state classification
zbMATH Keywords: missing data
zbMATH Keywords: least squares modeling
zbMATH Keywords: Gaussian state space modeling
zbMATH Keywords: trends
zbMATH Keywords: time varying variance
zbMATH Keywords: nonstationary covariance time series
zbMATH Keywords: inhomogeneous discrete processes
reviewed by: Jiří Anděl
describes a project that uses: AS 154
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4612-0761-0
OpenAlex ID: W1514443597
description: scientific article; zbMATH DE number 927555