Time series analysis by state space methods /
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.
| Main Authors: | , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Oxford :
Oxford University Press,
2012.
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| Edition: | Second edition. |
| Series: | Oxford statistical science series ;
38. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of 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