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Handbook of Econometrics Vols1-5 _ Chapter 50

Chapter 50 STATE-SPACE Contents Abstract 1. The state-space representation 2. The Kalman filter 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. Overview Derivation Forecasting Smoothed Interpretation Time-varying Other of the Kalman of the Kalman filter filter filter | Chapter 50 STATE-SPACE MODELS JAMES D. HAMILTON University of California San Diego Contents Abstract 3041 1. The state-space representation of a linear dynamic system 3041 2. The Kalman filter 3046 2.1. Overview of the Kalman filter 3047 2.2. Derivation of the Kalman filter 3048 2.3. Forecasting with the Kalman filter 3051 2.4. Smoothed inference 3051 2.5. Interpretation of the Kalman filter with non-normal disturbances 3052 2.6. Time-varying coefficient models 3053 2.7. Other extensions 3054 3. Statistical inference about unknown parameters using the Kalman filter 3055 3.1. Maximum likelihood estimation 3055 3.2. Identification 3057 3.3. Asymptotic properties of maximum likelihood estimates 3058 3.4. Confidence intervals for smoothed estimates and forecasts 3060 3.5. Empirical application - an analysis of the real interest rate 3060 4. Discrete-valued state variables 3062 4.1. Linear state-space representation of the Markov-switching model 3063 4.2. Optimal filter when the state variable follows a Markov chain 3064 4.3. Extensions 3067 4.4. Forecasting 3068 1 am grateful to Gongpil Choi Robert Engle and an anonymous referee for helpful comments and to the NSF for support under grant SES-8920752. Data and software used in this chapter can be obtained at no charge by writing James D. Hamilton Department of Economics 0508 UCSD La Jolla CA 92093-0508 USA. Alternatively data and software can be obtained by writing ICPSR Institute for Social Research P.O. Box 1248 Ann Arbor MI 48106 USA. Handbook of Econometrics Volume IV Edited by R.F. Engle and D.L. McFadden 1994 Elsevier Science B.V. All rights reserved J.D. Hamilton 3040 4.5. Smoothed probabilities 3069 4.6. Maximum likelihood estimation 3070 4.7. Asymptotic properties of maximum likelihood estimates 3071 4.8. Empirical application - another look at the real interest rate 3071 5. Non-normal and nonlinear state-space models 3073 5.1. Kitagawa s grid approximation for nonlinear non-normal state-space models 3073 5.2.