State-space models with regime switching : classical and Gibbs-sampling approaches with applications / Chang-Jin Kim and Charles R. Nelson.

Format:

Book

Author/Creator:

Kim, Chang-Jin, 1960- author.

Contributor:

Nelson, Charles R.

Language:

English

Subjects (All):

Economics--Mathematical models.

Economics.

State-space methods.

Heteroscedasticity.

Sampling (Statistics).

Econometrics.

Markov processes.

Econometric models.

Physical Description:

1 online resource (xii, 297 pages) : illustrations

Place of Publication:

Cambridge, Mass. : MIT Press, [1999]

System Details:

text file

Summary:

"Both state-space models and Markov-switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. One approach, in the classical framework, approximates the likelihood function; the other, in the Bayesian framework, uses Gibbs-sampling to simulate posterior distributions from data."--Jacket.

Contents:

1.1 State-Space Models and Markov Switching in Econometrics: A Brief History 2

1.2 Computer Programs and Data 4

I The Classical Approach 7

2 The Maximum Likelihood Estimation Method: Practical Issues 9

2.1 Maximum Likelihood Estimation and the Covariance Matrix of OML 9

2.2 The Prediction Error Decomposition and the Likelihood Function 11

2.3 Parameter Constraints and the Covariance Matrix of OML 13

3 State-Space Models and the Kalman Filter 19

3.1 Time-Varying-Parameter Models and the Kalman Filter 19

3.2 State-Space Models and the Kalman Filter 29

3.3 Application 1: A Decomposition of Real GDP and the Unemployment Rate into Stochastic Trend and Transitory Components 37

3.4 Application 2: An Application of the Time-Varying-Parameter Model to Modeling Changing Conditional Variance 44

3.5 Application 3: Stock and Watson's Dynamic Factor Model of the Coincident Economic Indicators 48

Appendix GAUSS Programs to Accompany Chapter 3 55

4 Markov-Switching Models 59

4.1 Introduction: Serially Uncorrelated Data and Switching 59

4.2 Serially Correlated Data and Markov Switching 64

4.3 Issues Related to Markov-Switching Models 68

4.4 Application 1: Hamilton's Markov-Switching Model of Business Fluctuations 78

4.5 Application 2: A Unit Root in a Three-State Markov-Switching Model of the Real Interest Rate 82

4.6 Application 3: A Three-State Markov-Switching Variance Model of Stock Returns 86

Appendix GAUSS Programs to Accompany Chapter 4 93

5 State-Space Models with Markov Switching 97

5.1 Specification of the Model 98

5.2 The Basic Filter and Estimation of the Model 99

5.3 Smoothing 106

5.4 An Evaluation of the Kim Filter and Approximate MLE 109

5.5 Application 1: Sources of Monetary Growth Uncertainty and Economic Activity 115

5.6 Application 2: Friedman's Plucking Model of Business Fluctuations and Implied Business Cycle Asymmetry 124

5.7 Application 3: A Dynamic Factor Model with Markov Switching: Business Cycle Turning Points and a New Coincident Index 126

Appendix GAUSS Programs to Accompany Chapter 5 133

6 State-Space Models with Heteroskedastic Disturbances 139

6.1 State-Space Models with ARCH Disturbances 140

6.2 State-Space Models with Markov-Switching Heteroskedasticity 146

6.3 Application 1: The Link between the Inflation Rate and Inflation Uncertainty 151

6.4 Application 2: Transient Fads and the Crash of '87 in the U.S. Stock Market 157

Appendix GAUSS Programs to Accompany Chapter 6 166

II The Gibbs-Sampling Approach 169

7 An Introduction to Bayesian Inference and Gibbs-Sampling 171

7.1 Classical versus Bayesian Analysis: Fundamental Differences 171

7.2 Bayesian Analysis: An Introduction 173

7.3 Gibbs-Sampling: Motivation and Basic Idea 178

7.4 Examples of Gibbs-Sampling in Econometrics 180

Appendix GAUSS Programs to Accompany Chapter 7 188

8 State-Space Models and Gibbs-Sampling 189

8.1 Generating the State Vector When Q Is Positive-Definite 190

8.2 Generating the State Vector When Q Is Singular: A Generalization 194

8.3 Application 1: A Gibbs-Sampling Approach to a Linear Dynamic Factor Model and a New Coincident Index 196

Appendix GAUSS Program to Accompany Chapter 8 205

9 Markov-Switching Models and Gibbs-Sampling 209

9.1 A Basic Model and the Bayesian Gibbs-Sampling Approach 209

9.2 Application 1: A Three-State Markov-Switching Variance Model of Stock Returns 219

9.3 Application 2: A Three-State Markov Switching Mean-Variance Model of the Real Interest Rate 229

Appendix GAUSS Programs to Accompany Chapter 9 236

10 State-Space Models with Markov Switching and Gibbs-Sampling 237

10.1 General Framework 237

10.2 Application 1: Business Cycle Turning Points and a New Coincident Index 241

10.3 Application 2: Business Cycle Duration Dependence within a Dynamic Factor Model: An Advantage of the Gibbs-Sampling Approach over the Classical Approach 257

10.4 Application 3: An Unobserved Components Model of the Long-Run U.S./U.K. Real Exchange Rate with Heteroskedasticity 266

Appendix GAUSS Program to Accompany Chapter 10 271

11 Gibbs-Sampling and Parameter Uncertainty: Testing for Mean Reversion in Heteroskedastic Data 275

11.1 Alternative Ways of Incorporating Parameter Uncertainty 275

11.2 Variance Ratio Tests of Mean Reversion: A Review 278

11.3 Historical Pattern of Heteroskedasticity and the Sampling Distribution of the Variance Ratio Statistic 279

11.4 New Tests of Mean Reversion in the Presence of Heteroskedasticity 284

Appendix GAUSS Programs to Accompany Chapter 11 292.

Notes:

OCLC-licensed vendor bibliographic record.

ISBN:

9780585087160

0585087164

9780262277112

0262277115

9780262277761

026227776X

OCLC:

43475778

Access Restriction:

Restricted for use by site license.