Time series analysis by state space methods / J. Durbin, S. J. Koopman.

Format:

Book

Author/Creator:

Durbin, J. (James), 1923-

Contributor:

Koopman, S. J. (Siem Jan)

Series:

Oxford statistical science series ; 38.

Oxford statistical science series ; no. 38

Language:

English

Subjects (All):

State-space methods.

Time-series analysis.

Physical Description:

1 online resource (401 p.)

Edition:

2nd ed.

Place of Publication:

Oxford : Oxford University Press, 2012.

Language Note:

English

Summary:

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 themain analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions to this second e

Contents:

Cover Page; Title Page; Copyright Page; Dedication; Preface to Second Edition; Preface to First Edition; 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; 2.2.1 The Kalman filter; 2.2.2 Regression lemma; 2.2.3 Bayesian treatment; 2.2.4 Minimum variance linear unbiased treatment; 2.2.5 Illustration; 2.3 Forecast errors

2.3.1 Cholesky decomposition2.3.2 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 checking2.12.1 Diagnostic tests for forecast errors; 2.12.2 Detection of outliers and structural breaks; 2.12.3 Illustration; 2.13 Exercises; 3. Linear state space models; 3.1 Introduction; 3.2 Univariate structural time series models; 3.2.1 Trend component; 3.2.2 Seasonal component; 3.2.3 Basic structural time series model; 3.2.4 Cycle component; 3.2.5 Explanatory variables and intervention effects; 3.2.6 STAMP; 3.3 Multivariate structural time series models; 3.3.1 Homogeneous models; 3.3.2 Common levels; 3.3.3 Latent risk model; 3.4 ARMA models and ARIMA models

3.5 Exponential smoothing3.6 Regression models; 3.6.1 Regression with time-varying coefficients; 3.6.2 Regression with ARMA errors; 3.7 Dynamic factor models; 3.8 State space models in continuous time; 3.8.1 Local level model; 3.8.2 Local linear trend model; 3.9 Spline smoothing; 3.9.1 Spline smoothing in discrete time; 3.9.2 Spline smoothing in continuous time; 3.10 Further comments on state space analysis; 3.10.1 State space versus Box-Jenkins approaches; 3.10.2 Benchmarking; 3.10.3 Simultaneous modelling of series from different sources; 3.11 Exercises

4. Filtering, smoothing and forecasting4.1 Introduction; 4.2 Basic results in multivariate regression theory; 4.3 Filtering; 4.3.1 Derivation of the Kalman filter; 4.3.2 Kalman filter recursion; 4.3.3 Kalman filter for models with mean adjustments; 4.3.4 Steady state; 4.3.5 State estimation errors and forecast errors; 4.4 State smoothing; 4.4.1 Introduction; 4.4.2 Smoothed state vector; 4.4.3 Smoothed state variance matrix; 4.4.4 State smoothing recursion; 4.4.5 Updating smoothed estimates; 4.4.6 Fixed-point and fixed-lag smoothers; 4.5 Disturbance smoothing; 4.5.1 Smoothed disturbances

4.5.2 Smoothed disturbance variance matrices

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-19-162719-4

0-19-162718-6

1-280-68002-4

9786613656957

OCLC:

794856270