Time Series Analysis by State Space Methods: Second Edition (Oxford Statistical Science Series)

Description

This new edition updates Durbin & Koopman's important text on the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbance terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions to this second edition include the filtering of nonlinear and non-Gaussian series. Part I of the book obtains the mean and variance of the state, of a variable intended to measure the effect of an interaction and of regression coefficients, in terms of the observations. Part II extends the treatment to nonlinear and non-normal models. For these, analytical solutions are not available so methods are based on simulation. 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 A B C D E F G H J K L M N O P Q R S T U V W Y Z Subject Index A B C D E F G H I K L M N O P Q R S T U V W