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Smoothness priors analysis of time series. (English) Zbl 0853.62069
Lecture Notes in Statistics (Springer). 116. New York, NY: Springer. x, 261 p. (1996).
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.
Reviewer: J.Anděl (Praha)

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62F15 Bayesian inference
Software:
AS 154
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