Chapter 50
STATE-SPACE MODELS*
JAMES D. HAMILTON
University of California, San Diego
Contents
Abstract
1. The state-space representation of a linear dynamic system
2. The Kalman filter
2.1. Overview of the Kalman filter
2.2. Derivation of the Kalman filter
2.3. Forecasting with the Kalman filter
2.4. Smoothed inference
2.5. Interpretation of the Kalman filter with non-normal disturbances
2.6. Time-varying coefficient models
2.7. Other extensions
3. Statistical inference about unknown parameters using the
Kalman filter
3.1. Maximum likelihood estimation
3.2. Identification
3.3. Asymptotic properties of maximum likelihood estimates
3.4. Confidence intervals for smoothed estimates and forecasts
3.5. Empirical application - an analysis of the real interest rate
4. Discrete-valued state variables
4.1. Linear state-space representation of the Markov-switching model
4.2. Optimal filter when the state variable follows a Markov chain
4.3. Extensions
4.4. Forecasting
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