Time Series Analysis by State Space Methods

About this book

This second 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.

Contents

1: Introduction

Part I: The linear state space model
2: Local level model
3: Linear Gaussian state space models
4: Filtering, smoothing and forecasting
5: Initialisation of Filter and smoother
6: Further computational aspects
7: Maximum likelihood estimation of parameters
8: Illustrations of the use of the linear Gaussian model

Part II: Non-Gaussian and nonlinear state space models
9: Special cases of nonlinear and non-Gaussian models
10: Approximate filtering and smoothing
11: Importance sampling for smoothing
12: Particle filtering
13: Bayesian estimation of parameters
14: Non-Gaussian and nonlinear illustrations

Subject Index

Customer Reviews

Biography

James Durbin was Professor of Statistics at the London School of Economics, President of the Royal Statistical Society and President of the International Statistical Institute. He was awarded the society's bronze, silver and gold medals for his contribution to statistics. He is a fellow of the British Academy.

Siem Jan Koopman has been Professor of Econometrics at the Free University in Amsterdam and research fellow at the Tinbergen Institute since 1999. He fullfills editorial duties at the "Journal of Applied Econometrics", the "Journal of Forecasting", the "Journal of Multivariate Analysis" and "Statistica Sinica".