The presentation will cover most of Durbin and Koopman’s (2002) Time Series Analysis by State Space Methods, with some additions from Harvey’s (1989) Forecasting, structural time series and the Kalman filter and West and Harrison’s (1997) Bayesian Forecasting and Dynamic Models.
(136 pages)
Preface 1 Introduction 1 1.1 State-Space Models 1.2 Kalman Filtering with the Local Linear Model 1.3 Kalman Filtering with the Time-Varying Coefficients Model 1.4 Kalman Smoothing 1.5 Kalman Smoothing with the Local Linear Model 1.6 Forecasts and Missing Data 1.7 RATS Tips and Tricks Examples: 1.1 Kalman Filter: Nile Data 1.2 Kalman Filter: Drug Sales Data 1.3 Kalman Filter: Time-Varying Coefficients Model 1.4 Kalman Smoothing: Nile Data 1.5 Kalman Smoothing: Estimated Errors 1.6 Missing Data 1.7 Out of Sample Forecasting 2 More States 2.1 Kalman Filter in Matrix Form 2.2 ARMA Processes 2.3 Local Trend Model 2.4 Seasonals Examples: 2.1 Local Level vs Local Trend Model 3 Estimating Variances 3.1 The Likelihood Function 3.2 Estimating the Local Level Model 3.3 Estimating the Local Trend Model 3.4 Diagnostics Examples: 3.1 Estimating the Local Level Model 3.2 Estimating the Local Trend Model 3.3 Diagnostics 4 Initialization 4.1 Ergodic Solution 4.2 Diffuse Prior 4.3 Mixed Stationary and Non-Stationary Models 5 Practical Examples with a Single Observable 5.1 Basic Structural Models 5.2 Trend plus Stationary Cycle Examples: 5.1 Airline Data 5.2 Trend plus Stationary Cycle Model 6 Practical Examples with Multiple Observables 6.1 Indicator Models 6.2 Multivariate H-P Filter Examples: 6.1 Stock-Watson Indicator Model 6.2 Bivariate H-P Filter 7 Interpolation and Distribution 7.1 Linear Model 7.2 Log-Linear Model 7.3 Proportional Denton Method Examples: 7.1 Proportional Denton method 8 Non-Normal Errors 8.1 Stochastic volatility model 8.2 t Distributed Errors Examples: 8.1 Stochastic Volatility Model 8.2 Fat-Tailed Errors 9 Simulations 9.1 Simulations 10 DSGE: Setting Up and Solving Models 10.1 Requirements 10.2 Adapting to different information sets 10.3 Non-linear models 10.4 Unit Roots 10.5 Dynare scripts 11 DSGE: Applications 11.1 Simulations 11.2 Impulse Responses Examples: 11.1 DSGE Simulation 11.2 DSGE Impulse Response Functions 12 DSGE: Estimation 12.1 Maximum Likelihood 12.2 Bayesian Methods 12.3 Tips and Tricks Examples: 12.1 Maximum Likelihood: Hyperinflation Model 12.2 Maximum Likelihood: Hansen RBC 12.3 Bayesian Estimation: Hyperinflation Model A Probability Distributions A.1 Uniform A.2 Univariate Normal A.3 Beta distribution A.4 Gamma Distribution A.5 Bernoulli Distribution A.6 Multivariate Normal B Properties of Multivariate Normals C Non-Standard Matrix Calculations D A General Result on Smoothing E Generalized Ergodic Initialization F Quasi-Maximum Likelihood Estimations (QMLE) Bibliography Index