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Smoothness Priors Analysis of Time Series

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 hyperpa...

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Bibliographic Details
Main Authors: Kitagawa, Genshiro, Gersch, Will (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1996, 1996
Edition:1st ed. 1996
Series:Lecture Notes in Statistics
Subjects:
Mathematical Analysis
Statistics 
Analysis
Statistics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 10.4 Smoothing the Periodogram
  • 10.5 The Maximum Daily Temperature Data
  • 11 Modeling Scalar Nonstationary Covariance Time Series
  • 11.1 Introduction
  • 11.2 A Time Varying AR Coefficient Model
  • 11.3 A State Space Model
  • 11.4 PARCOR Time Varying AR Modeling
  • 11.5 Examples
  • 12 Modeling Multivariate Nonstationary Covariance Time Series
  • 12.1 Introduction
  • 12.2 The Instantaneous Response-Orthogonal Innovations Model
  • 12.3 State Space Modeling
  • 12.4 Time Varying PARCOR VAR Modeling
  • 12.5 Examples
  • 13 Modeling Inhomogeneous Discrete Processes
  • 13.1 Nonstationary Discrete Process
  • 13.2 Nonstationary Binary Processes
  • 13.3 Nonstationary Poisson Process
  • 14 Quasi-Periodic Process Modeling
  • 14.1 The Quasi-periodic Model
  • 14.2 The Wolfer Sunspot Data
  • 14.3 The Canadian Lynx Data
  • 14.4 Other Examples
  • 14.5 Predictive Properties of Quasi-periodic Process Modeling
  • 15 Nonlinear Smoothing
  • 15.1 Introduction
  • 15.2 State Estimation
  • 6.3 Numerical Synthesis of the Algorithms
  • 6.4 The Gaussian Sum-Two Filter Formula Approximation
  • 6.5 A Monte Carlo Filtering and Smoothing Method
  • 6.6 A Derivation of the Kalman filter
  • 7 Applications of Linear Gaussian State Space Modeling
  • 7.1 AR Time Series Modeling
  • 7.2 Kullback-Leibler Computations
  • 7.3 Smoothing Unequally Spaced Data
  • 7.4 A Signal Extraction Problem
  • 8 Modeling Trends
  • 8.1 State Space Trend Models
  • 8.2 State Space Estimation of Smooth Trend
  • 8.3 Multiple Time Series Modeling: The Common Trend Plus Individual Component AR Model
  • 8.4 Modeling Trends with Discontinuities
  • 9 Seasonal Adjustment
  • 9.1 Introduction
  • 9.2 A State Space Seasonal Adjustment Model
  • 9.3 Smooth Seasonal Adjustment Examples
  • 9.4 Non-Gaussian Seasonal Adjustment
  • 9.5 Modeling Outliers
  • 9.6 Legends
  • 10 Estimation of Time Varying Variance
  • 10.1Introduction and Background
  • 10.2 Modeling Time-Varying Variance
  • 10.3 The Seismic Data
  • 1 Introduction
  • 1.1 Background
  • 1.2 What is in the Book
  • 1.3 Time Series Examples
  • 2 Modeling Concepts and Methods
  • 2.1 Akaike’s AIC: Evaluating Parametric Models
  • 2.2 Least Squares Regression by Householder Transformation
  • 2.3 Maximum Likelihood Estimation and an Optimization Algorithm
  • 2.4 State Space Methods
  • 3 The Smoothness Priors Concept
  • 3.1 Introduction
  • 3.2 Background, History and Related Work
  • 3.3 Smoothness Priors Bayesian Modeling
  • 4 Scalar Least Squares Modeling
  • 4.1 Estimating a Trend
  • 4.2 The Long AR Model
  • 4.3 Transfer Function Estimation
  • 5 Linear Gaussian State Space Modeling
  • 5.1 Introduction
  • 5.2 Standard State Space Modeling
  • 5.3 Some State Space Models
  • 5.4 Modeling With Missing Observations
  • 5.5 Unequally Spaced Observations
  • 5.6 An Information Square-Root Filter/Smoother
  • 6 Contents General State Space Modeling
  • 6.1 Introduction
  • 6.2 The General State Space Model
  • 15.3 A One Dimensional Problem
  • 15.4 A Two Dimensional Problem
  • 16 Other Applications
  • 16.1 A Large Scale Decomposition Problem
  • 16.2 Markov State Classification
  • 16.3 SPVAR Modeling for Spectrum Estimation
  • References
  • Author Index

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