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Book Cover
E-book
Author Durbin, J. (James), 1923-2012, author.

Title Time series analysis by state space methods / James Durbin and Siem Jan Koopman
Edition Second edition
Published Oxford : Oxford University Press, 2012

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Description 1 online resource (xxi, 346 pages) : illustrations
Series Oxford statistical science series ; 38
Oxford statistical science series ; 38.
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
Summary This is a comprehensive treatment of the state space approach to time series analysis. A distinguishing feature of state space time series models is that observations are regarded as made up of distinct components, which are each modelled separately
Bibliography Includes bibliographical references and indexes
Notes Print version record
Subject Time-series analysis.
State-space methods.
MATHEMATICS -- Probability & Statistics -- Time Series.
State-space methods
Time-series analysis
Form Electronic book
Author Koopman, S. J. (Siem Jan), author.
ISBN 9780191627187
0191627186
9780191774881
019177488X
019964117X
9780199641178