This workbook covers a broad range of topics for models with various types of breaks or regime shifts. In some cases, models with breaks are used as diagnostics for models with fixed coefficients. If the fixed coefficient model is adequate, we would expect to reject a similar model that allows for breaks, either in the coefficients or in the variances. For these uses, the model with the breaks isn’t being put forward as a model of reality, but simply as an alternative for testing purposes.

Increasingly, however, models with breaks are being put forward as a description of the process itself. There are two broad classes of such models: those with observable regimes and those with hidden regimes. Models with observable criteria include Threshold Autoregressions and VAR's and Smooth Threshold Models. In all these models, there is a threshold trigger which causes a shift of the process from one regime to another, typically when an observable series moves across an (unknown) boundary.

The remaining seven chapters cover models with hidden regimes, that is models where there is no observable criterion which determines to which regime a data point belongs. Instead, we have a model which describes the behavior of the observables in each regime, and a second model which describes the (unconditional) probabilities of the regimes, which we combine using Bayes rule to infer the posterior probability of the regimes. These start off with simple models and work toward increasingly complex models such as MS-VAR's.

The final two chapters look at Markov switching in models where exact likelihoods can’t be computed, requiring approximations to the likelihood. Chapter 12 examines state-space models with Markov switching, while Chapter 13 is devoted to switching ARCH and GARCH models.

The second edition adds over 100 pages, with new coverage of the ICSS test for variance breaks (Section 2.1), the “fixed regressor bootstrap” (Section 3.3), increased coverage of computation of non-linear impulse response functions in various threshold models (Sections 4.4, 5.2.3 and 6.3) and a completely rewritten section on Threshold VAR’s (5.2). We’ve reworked the various Markov switching support procedures, and the updated chapters on Markov Switching models and their examples have been revised to reflect that. In particular, Chapter 10 on Markov Switching Multivariate Regressions now has a (very) detailed description of the process of computing regime-specific impulse response functions with error bands.

Finally, the section on Markov Switching GARCH models (Section 13.2) has been completely rewritten to explain the difference between the more accurate “Dueker filter” and the more commonly used “Gray filter” with application to the same data set to demonstrate that. It’s also shown that each of the filters at times may fail (rather badly) to provide an adequate approximation to the log likelihood, producing possibly misleading results.

(342 pages, 40 examples)

1.2 Breaks in Static Models

1.3 Breaks in Dynamic Models

1.4 RATS Tips and Tricks

2.2 Rolling Sample Estimates

3.1.1 Linear Least Squares

3.1.2 GMM

3.2 Outliers and Shifts

3.2.1 Linear Least Squares

3.2.2 ARIMA models

3.2.3 GARCH models

3.3 Fixed Regressor Bootstrap

4.2 Testing

4.2.1 Arranged Autoregression Test

4.2.2 Direct Threshold Tests

4.3 Forecasting

4.4 Non-linear Impulse Responses

4.5 Tips and Tricks

5.2}Threshold \textsc {var

5.2.1 Tsay(1998) interest rates example

5.2.2 Balke(2000) Credit Regimes

5.2.3 Impulse Response Functions

5.3 Threshold Cointegration

6.2 Estimation

6.3 Forecasts and Impulse Responses

6.4 More Complicated Models

7.2 EM Estimation

7.3 Bayesian MCMC

7.3.1 Label Switching

8.2 Common Concepts

8.2.1 Prediction Step

8.2.2 Update Step

8.2.3 Smoothing

8.2.4 Simulation of Regimes

8.2.5 Pre-Sample Regime Probabilities

8.2.6 Pathologies

8.3 Estimation

8.3.1 Simple Example

8.3.2 Maximum Likelihood

8.3.3 EM

8.3.4 MCMC (Gibbs Sampling)

9.2 The example

9.2.1 Maximum Likelihood

9.2.2 EM

9.2.3 MCMC (Gibbs Sampling)

10.1.1 Impulse Response Functions

10.2 The example

10.2.1 Maximum Likelihood

10.2.2 EM

10.2.3 MCMC (Gibbs Sampling)

10.3 Systems Regression with Fixed Coefficients

11.1.1 MSVARSETUP procedures

11.2 The example

11.2.1 Maximum Likelihood

11.2.2 EM

11.2.3 MCMC (Gibbs Sampling)

12.2 The Kim Filter

12.2.1 Lam Model by Kim Filter

12.2.2 Time-Varying Parameters Model by Kim Filter

12.3 Estimation with MCMC

12.3.1 Lam Model by MCMC

12.3.2 Time-varying parameters by MCMC

13.1.1 Estimation by ML

13.1.2 Estimation by MCMC

13.2 Markov Switching GARCH

13.2.1 The Example

13.2.2 Dueker Filter

13.2.3 Gray Filter

F.2 Beta distribution

F.3 Dirichlet distribution

F.4 (Scaled) Inverse Chi-Squared Distribution

F.5 Gamma Distribution

F.6 Inverse Gamma Distribution

F.7 Bernoulli Distribution

F.8 Multivariate Normal

F.9 Wishart Distribution

F.10 Inverse Wishart Distribution