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SSM Sample Chapter.pdf- Sample chapter
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State Space and DSGE Course
Workbook Preface
The presentation covers 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.
Workbook Contents
(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 volatity 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