Time series analysis by state space methods /

Time series analysis by state space methods /

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Bibliographic Details
Author / Creator:Durbin, James.
Imprint:Oxford ; New York : Oxford University Press, 2001.
Description:xvii, 253 p. : ill. ; 25 cm.
Language:English
Series:Oxford statistical science series ; 24
Subject:
Time-series analysis.
State-space methods.
State-space methods.
Time-series analysis.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4505883
Hidden Bibliographic Details
Other authors / contributors:Koopman, S. J. (Siem Jan)
ISBN:0198523548 (acid-free paper)
Notes:Includes bibliographical references (p. [241]-247) and index.
Table of Contents:
  • 1. Introduction
  • 1.1. Basic ideas of state space analysis
  • 1.2. Linear Gaussian model
  • 1.3. Non-Gaussian and nonlinear models
  • 1.4. Prior knowledge
  • 1.5. Notation
  • 1.6. Other books on state space methods
  • 1.7. Website for the book
  • I. The Linear Gaussian State Space Model
  • 2. Local level model
  • 2.1. Introduction
  • 2.2. Filtering
  • 2.2.1. The Kalman Filter
  • 2.2.2. Illustration
  • 2.3. Forecast errors
  • 2.3.1. Cholesky decomposition
  • 2.3.2. Error recursions
  • 2.4. State smoothing
  • 2.4.1. Smoothed state
  • 2.4.2. Smoothed state variance
  • 2.4.3. Illustration
  • 2.5. Disturbance smoothing
  • 2.5.1. Smoothed observation disturbances
  • 2.5.2. Smoothed state disturbances
  • 2.5.3. Illustration
  • 2.5.4. Cholesky decomposition and smoothing
  • 2.6. Simulation
  • 2.6.1. Illustration
  • 2.7. Missing observations
  • 2.7.1. Illustration
  • 2.8. Forecasting
  • 2.8.1. Illustration
  • 2.9. Initialisation
  • 2.10. Parameter estimation
  • 2.10.1. Loglikelihood evaluation
  • 2.10.2. Concentration of loglikelihood
  • 2.10.3. Illustration
  • 2.11. Steady state
  • 2.12. Diagnostic checking
  • 2.12.1. Diagnostic tests for forecast errors
  • 2.12.2. Detection of outliers and structural breaks
  • 2.12.3. Illustration
  • 2.13. Appendix: Lemma in multivariate normal regression
  • 3. Linear Gaussian state space models
  • 3.1. Introduction
  • 3.2. Structural time series models
  • 3.2.1. Univariate models
  • 3.2.2. Multivariate models
  • 3.2.3. Stamp
  • 3.3. ARMA models and ARIMA models
  • 3.4. Exponential smoothing
  • 3.5. State space versus Box-Jenkins approaches
  • 3.6. Regression with time-varying coefficients
  • 3.7. Regression with ARMA errors
  • 3.8. Benchmarking
  • 3.9. Simultaneous modelling of series from different sources
  • 3.10. State space models in continuous time
  • 3.10.1. Local level model
  • 3.10.2. Local linear trend model
  • 3.11. Spline smoothing
  • 3.11.1. Spline smoothing in discrete time
  • 3.11.2. Spline smoothing in continuous time
  • 4. Filtering, smoothing and forecasting
  • 4.1. Introduction
  • 4.2. Filtering
  • 4.2.1. Derivation of Kalman filter
  • 4.2.2. Kalman filter recursion
  • 4.2.3. Steady state
  • 4.2.4. State estimation errors and forecast errors
  • 4.3. State smoothing
  • 4.3.1. Smoothed state vector
  • 4.3.2. Smoothed state variance matrix
  • 4.3.3. State smoothing recursion
  • 4.4. Disturbance smoothing
  • 4.4.1. Smoothed disturbances
  • 4.4.2. Fast state smoothing
  • 4.4.3. Smoothed disturbance variance matrices
  • 4.4.4. Disturbance smoothing recursion
  • 4.5. Covariance matrices of smoothed estimators
  • 4.6. Weight functions
  • 4.6.1. Introduction
  • 4.6.2. Filtering weights
  • 4.6.3. Smoothing weights
  • 4.7. Simulation smoothing
  • 4.7.1. Simulating observation disturbances
  • 4.7.2. Derivation of simulation smoother for observation disturbances
  • 4.7.3. Simulation smoothing recursion
  • 4.7.4. Simulating state disturbances
  • 4.7.5. Simulating state vectors
  • 4.7.6. Simulating multiple samples
  • 4.8. Missing observations
  • 4.9. Forecasting
  • 4.10. Dimensionality of observational vector
  • 4.11. General matrix form for filtering and smoothing
  • 5. Initialisation of filter and smoother
  • 5.1. Introduction
  • 5.2. The exact initial Kalman filter
  • 5.2.1. The basic recursions
  • 5.2.2. Transition to the usual Kalman filter
  • 5.2.3. A convenient representation
  • 5.3. Exact initial state smoothing
  • 5.3.1. Smoothed mean of state vector
  • 5.3.2. Smoothed variance of state vector
  • 5.4. Exact initial disturbance smoothing
  • 5.5. Exact initial simulation smoothing
  • 5.6. Examples of initial conditions for some models
  • 5.6.1. Structural time series models
  • 5.6.2. Stationary ARMA models
  • 5.6.3. Nonstationary ARIMA models
  • 5.6.4. Regression model with ARMA errors
  • 5.6.5. Spline smoothing
  • 5.7. Augmented Kalman filter and smoother
  • 5.7.1. Introduction
  • 5.7.2. Augmented Kalman filter
  • 5.7.3. Filtering based on the augmented Kalman filter
  • 5.7.4. Illustration: the local linear trend model
  • 5.7.5. Comparisons of computational efficiency
  • 5.7.6. Smoothing based on the augmented Kalman filter
  • 6. Further computational aspects
  • 6.1. Introduction
  • 6.2. Regression estimation
  • 6.2.1. Introduction
  • 6.2.2. Inclusion of coefficient vector in state vector
  • 6.2.3. Regression estimation by augmentation
  • 6.2.4. Least squares and recursive residuals
  • 6.3. Square root filter and smoother
  • 6.3.1. Introduction
  • 6.3.2. Square root form of variance updating
  • 6.3.3. Givens rotations
  • 6.3.4. Square root smoothing
  • 6.3.5. Square root filtering and initialisation
  • 6.3.6. Ilustration: local linear trend model
  • 6.4. Univariate treatment of multivariate series
  • 6.4.1. Introduction
  • 6.4.2. Details of univariate treatment
  • 6.4.3. Correlation between observation equations
  • 6.4.4. Computational efficiency
  • 6.4.5. Illustration: vector splines
  • 6.5. Filtering and smoothing under linear restrictions
  • 6.6. The algorithms of SsfPack
  • 6.6.1. Introduction
  • 6.6.2. The SsfPack function
  • 6.6.3. Illustration: spline smoothing
  • 7. Maximum likelihood estimation
  • 7.1. Introduction
  • 7.2. Likelihood evaluation
  • 7.2.1. Loglikelihood when initial conditions are known
  • 7.2.2. Diffuse loglikelihood
  • 7.2.3. Diffuse loglikelihood evaluated via augmented Kalman filter
  • 7.2.4. Likelihood when elements of initial state vector are fixed but unknown
  • 7.3. Parameter estimation
  • 7.3.1. Introduction
  • 7.3.2. Numerical maximisation algorithms
  • 7.3.3. The score vector
  • 7.3.4. The EM algorithm
  • 7.3.5. Parameter estimation when dealing with diffuse initial conditions
  • 7.3.6. Large sample distribution of maximum likelihood estimates
  • 7.3.7. Effect of errors in parameter estimation
  • 7.4. Goodness of fit
  • 7.5. Diagnostic checking
  • 8. Bayesian analysis
  • 8.1. Introduction
  • 8.2. Posterior analysis of state vector
  • 8.2.1. Posterior analysis conditional on parameter vector
  • 8.2.2. Posterior analysis when parameter vector is unknown
  • 8.2.3. Non-informative priors
  • 8.3. Markov chain Monte Carlo methods
  • 9. Illustrations of the use of the linear Gaussian model
  • 9.1. Introduction
  • 9.2. Structural time series models
  • 9.3. Bivariate structural time series analysis
  • 9.4. Box-Jenkins analysis
  • 9.5. Spline smoothing
  • 9.6. Approximate methods for modelling volatility
  • II. Non-Gaussian And Nonlinear State Space Models
  • 10. Non-Gaussian and nonlinear state space models
  • 10.1. Introduction
  • 10.2. The general non-Gaussian model
  • 10.3. Exponential family models
  • 10.3.1. Poisson density
  • 10.3.2. Binary density
  • 10.3.3. Binomial density
  • 10.3.4. Negative binomial density
  • 10.3.5. Multinomial density
  • 10.4. Heavy-tailed distributions
  • 10.4.1. t-Distribution
  • 10.4.2. Mixture of normals
  • 10.4.3. General error distribution
  • 10.5. Nonlinear models
  • 10.6. Financial models
  • 10.6.1. Stochastic volatility models
  • 10.6.2. General autoregressive conditional heteroscedasticity
  • 10.6.3. Durations: exponential distribution
  • 10.6.4. Trade frequencies: Poisson distribution
  • 11. Importance sampling
  • 11.1. Introduction
  • 11.2. Basic ideas of importance sampling
  • 11.3. Linear Gaussian approximating models
  • 11.4. Linearisation based on first two derivatives
  • 11.4.1. Exponentional family models
  • 11.4.2. Stochastic volatility model
  • 11.5. Linearisation based on the first derivative
  • 11.5.1. t-distribution
  • 11.5.2. Mixture of normals
  • 11.5.3. General error distribution
  • 11.6. Linearisation for non-Gaussian state components
  • 11.6.1. t-distribution for state errors
  • 11.7. Linearisation for nonlinear models
  • 11.7.1. Multiplicative models
  • 11.8. Estimating the conditional mode
  • 11.9. Computational aspects of importance sampling
  • 11.9.1. Introduction
  • 11.9.2. Practical implementation of importance sampling
  • 11.9.3. Antithetic variables
  • 11.9.4. Diffuse initialisation
  • 11.9.5. Treatment of t-distribution without importance sampling
  • 11.9.6. Treatment of Gaussian mixture distributions without importance sampling
  • 12. Analysis from a classical standpoint
  • 12.1. Introduction
  • 12.2. Estimating conditional means and variances
  • 12.3. Estimating conditional densities and distribution functions
  • 12.4. Forecasting and estimating with missing observations
  • 12.5. Parameter estimation
  • 12.5.1. Introduction
  • 12.5.2. Estimation of likelihood
  • 12.5.3. Maximisation of loglikelihood
  • 12.5.4. Variance matrix of maximum likelihood estimate
  • 12.5.5. Effect of errors in parameter estimation
  • 12.5.6. Mean square error matrix due to simulation
  • 12.5.7. Estimation when the state disturbances are Gaussian
  • 12.5.8. Control variables
  • 13. Analysis from a Bayesian standpoint
  • 13.1. Introduction
  • 13.2. Posterior analysis of functions of the state vector
  • 13.3. Computational aspects of Bayesian analysis
  • 13.4. Posterior analysis of parameter vector
  • 13.5. Markov chain Monte Carlo methods
  • 14. Non-Gaussian and nonlinear illustrations
  • 14.1. Introduction
  • 14.2. Poisson density: van drivers killed in Great Britain
  • 14.3. Heavy-tailed density: outlier in gas consumption in UK
  • 14.4. Volatility: pound/dollar daily exchange rates
  • 14.5. Binary density: Oxford-Cambridge boat race
  • 14.6. Non-Gaussian and nonlinear analysis using SsfPack
  • References
  • Author index
  • Subject index
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