Handbook of Econometrics Vols1-5 _ Chapter 50

Chapter 50 STATE-SPACE Contents Abstract 1. The state-space representation 2. The Kalman filter . . . . . . . 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 . Overview of the Kalman filter 3047 . Derivation of the Kalman filter 3048 . Forecasting with the Kalman filter 3051 . Smoothed inference 3051 . Interpretation of the Kalman filter with non-normal disturbances 3052 . Time-varying coefficient models 3053 . Other extensions 3054 3. Statistical inference about unknown parameters using the Kalman filter 3055 . Maximum likelihood estimation 3055 . Identification 3057 . Asymptotic properties of maximum likelihood estimates 3058 . Confidence intervals for smoothed estimates and forecasts 3060 . Empirical application - an analysis of the real interest rate 3060 4. Discrete-valued state variables 3062 . Linear state-space representation of the Markov-switching model 3063 . Optimal filter when the state variable follows a Markov chain 3064 . Extensions 3067 . 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 . Box 1248 Ann Arbor MI 48106 USA. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved . Hamilton 3040 . Smoothed probabilities 3069 . Maximum likelihood estimation 3070 . Asymptotic properties of maximum likelihood estimates 3071 . Empirical application - another look at the real interest rate 3071 5. Non-normal and nonlinear state-space models 3073 . Kitagawa s grid approximation for nonlinear non-normal state-space models 3073 .