Time Series Analysis by State Space Methods

Cover
Contents
1. Introduction
	1.1 Basic ideas of state space analysis
	1.2 Linear models
	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
PART I: THE LINEAR STATE SPACE MODEL
	2. Local level model
		2.1 Introduction
		2.2 Filtering
		2.3 Forecast errors
		2.4 State smoothing
		2.5 Disturbance smoothing
		2.6 Simulation
		2.7 Missing observations
		2.8 Forecasting
		2.9 Initialisation
		2.10 Parameter estimation
		2.11 Steady state
		2.12 Diagnostic checking
		2.13 Exercises
	3. Linear state space models
		3.1 Introduction
		3.2 Univariate structural time series models
		3.3 Multivariate structural time series models
		3.4 ARMA models and ARIMA models
		3.5 Exponential smoothing
		3.6 Regression models
		3.7 Dynamic factor models
		3.8 State space models in continuous time
		3.9 Spline smoothing
		3.10 Further comments on state space analysis
		3.11 Exercises
	4. Filtering, smoothing and forecasting
		4.1 Introduction
		4.2 Basic results in multivariate regression theory
		4.3 Filtering
		4.4 State smoothing
		4.5 Disturbance smoothing
		4.6 Other state smoothing algorithms
		4.7 Covariance matrices of smoothed estimators
		4.8 Weight functions
		4.9 Simulation smoothing
		4.10 Missing observations
		4.11 Forecasting
		4.12 Dimensionality of observational vector
		4.13 Matrix formulations of basic results
		4.14 Exercises
	5. Initialisation of filter and smoother
		5.1 Introduction
		5.2 The exact initial Kalman filter
		5.3 Exact initial state smoothing
		5.4 Exact initial disturbance smoothing
		5.5 Exact initial simulation smoothing
		5.6 Examples of initial conditions for some models
		5.7 Augmented Kalman filter and smoother
	6. Further computational aspects
		6.1 Introduction
		6.2 Regression estimation
		6.3 Square root filter and smoother
		6.4 Univariate treatment of multivariate series
		6.5 Collapsing large observation vectors
		6.6 Filtering and smoothing under linear restrictions
		6.7 Computer packages for state space methods
	7. Maximum likelihood estimation of parameters
		7.1 Introduction
		7.2 Likelihood evaluation
		7.3 Parameter estimation
		7.4 Goodness of fit
		7.5 Diagnostic checking
	8. Illustrations of the use of the linear model
		8.1 Introduction
		8.2 Structural time series models
		8.3 Bivariate structural time series analysis
		8.4 Box–Jenkins analysis
		8.5 Spline smoothing
		8.6 Dynamic factor analysis
PART II: NON-GAUSSIAN AND NONLINEAR STATE SPACE MODELS
	9. Special cases of nonlinear and non-Gaussian models
		9.1 Introduction
		9.2 Models with a linear Gaussian signal
		9.3 Exponential family models
		9.4 Heavy-tailed distributions
		9.5 Stochastic volatility models
		9.6 Other financial models
		9.7 Nonlinear models
	10. Approximate filtering and smoothing
		10.1 Introduction
		10.2 The extended Kalman filter
		10.3 The unscented Kalman filter
		10.4 Nonlinear smoothing
		10.5 Approximation via data transformation
		10.6 Approximation via mode estimation
		10.7 Further advances in mode estimation
		10.8 Treatments for heavy-tailed distributions
	11. Importance sampling for smoothing
		11.1 Introduction
		11.2 Basic ideas of importance sampling
		11.3 Choice of an importance density
		11.4 Implementation details of importance sampling
		11.5 Estimating functions of the state vector
		11.6 Estimating loglikelihood and parameters
		11.7 Importance sampling weights and diagnostics
	12. Particle filtering
		12.1 Introduction
		12.2 Filtering by importance sampling
		12.3 Sequential importance sampling
		12.4 The bootstrap particle filter
		12.5 The auxiliary particle filter
		12.6 Other implementations of particle filtering
		12.7 Rao–Blackwellisation
	13. Bayesian estimation of parameters
		13.1 Introduction
		13.2 Posterior analysis for linear Gaussian model
		13.3 Posterior analysis for a nonlinear non-Gaussian model
		13.4 Markov chain Monte Carlo methods
	14. Non-Gaussian and nonlinear illustrations
		14.1 Introduction
		14.2 Nonlinear decomposition: UK visits abroad
		14.3 Poisson density: van drivers killed in Great Britain
		14.4 Heavy-tailed density: outlier in gas consumption
		14.5 Volatility: pound/dollar daily exchange rates
		14.6 Binary density: Oxford–Cambridge boat race
References
Author Index
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	B
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Subject Index
	A
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