State Space and DSGE Course

Workbook Preface

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.

Workbook Contents

(143 pages, 24 examples)

Preface

1 Introduction

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
Example 1.1 Kalman Filter: Nile Data
Example 1.2 Kalman Filter: Drug Sales Data
Example 1.3 Kalman Filter: Time-Varying Coefficients Model
Example 1.4 Kalman Smoothing: Nile Data
Example 1.5 Kalman Smoothing: Estimated Errors
Example 1.6 Missing Data
Example 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
Example 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
Example 3.1 Estimating the Local Level Model
Example 3.2 Estimating the Local Trend Model
Example 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
Example 5.1 Airline Data
Example 5.2 Trend plus Stationary Cycle Model

6 Practical Examples with Multiple Observables

6.1 Indicator Models
6.2 Multivariate H-P Filter
Example 6.1 Stock-Watson Indicator Model
Example 6.2 Bivariate H-P Filter

7 Interpolation and Distribution

7.1 Linear Model
7.2 Log-Linear Model
7.3 Proportional Denton Method
Example 7.1 Proportional Denton method

8 Non-Normal Errors

8.1 Stochastic volatity model
8.2 t Distributed Errors
Example 8.1 Stochastic Volatility Model
Example 8.2 Fat-Tailed Errors

9 Simulations

Example 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
Example 11.1 DSGE Simulation
Example 11.2 DSGE Impulse Response Functions

12 DSGE: Estimation

12.1 Maximum Likelihood
12.2 Bayesian Methods
12.3 Tips and Tricks
Example 12.1 Maximum Likelihood: Hyperinflation Model
Example 12.2 Maximum Likelihood: Hansen RBC
Example 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